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MATH-ETE-DATA

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train · 72.1k rows

problem stringlengths 16 2.02k	solution stringlengths 29 4.45k	answer stringlengths 1 69	subject stringclasses 7 values	level int64 1 5	unique_id stringlengths 20 40	idx int64 0 7k	ete_solution stringlengths 198 2.15k	gen_length int64 512 512	num_steps int64 14 212	pareto_index int64 0 33	sampling_params stringclasses 34 values	worst_case_steps int64 15 232	best_case_steps int64 13 202	explore_failures int64 0 0	explore_count int64 0 10	solution_reward float64 1 1	extracted_pred_answer stringlengths 10 264	extracted_gold_answer stringlengths 10 168	is_solution_correct bool 1 class	sequence_0 listlengths 512 512	sequence_1 listlengths 512 512	sequence_2 listlengths 512 512	sequence_3 listlengths 512 512	sequence_4 listlengths 512 512	sequence_5 listlengths 512 512	sequence_6 listlengths 512 512	sequence_7 listlengths 512 512	sequence_8 listlengths 512 512	sequence_9 listlengths 512 512	sequence_10 listlengths 512 512	sequence_11 listlengths 512 512	sequence_12 listlengths 512 512	sequence_13 listlengths 512 512	sequence_14 listlengths 512 512	sequence_15 listlengths 512 512 ⌀	sequence_16 listlengths 512 512 ⌀	sequence_17 listlengths 512 512 ⌀	sequence_18 listlengths 512 512 ⌀	sequence_19 listlengths 512 512 ⌀	sequence_20 listlengths 512 512 ⌀	sequence_21 listlengths 512 512 ⌀	sequence_22 listlengths 512 512 ⌀	sequence_23 listlengths 512 512 ⌀	sequence_24 listlengths 512 512 ⌀	sequence_25 listlengths 512 512 ⌀	sequence_26 listlengths 512 512 ⌀	sequence_27 listlengths 512 512 ⌀	sequence_28 listlengths 512 512 ⌀	sequence_29 listlengths 512 512 ⌀	sequence_30 listlengths 512 512 ⌀	sequence_31 listlengths 512 512 ⌀	sequence_32 listlengths 512 512 ⌀	sequence_33 listlengths 512 512 ⌀	sequence_34 listlengths 512 512 ⌀	sequence_35 listlengths 512 512 ⌀	sequence_36 listlengths 512 512 ⌀	sequence_37 listlengths 512 512 ⌀	sequence_38 listlengths 512 512 ⌀	sequence_39 listlengths 512 512 ⌀	sequence_40 listlengths 512 512 ⌀	sequence_41 listlengths 512 512 ⌀	sequence_42 listlengths 512 512 ⌀	sequence_43 listlengths 512 512 ⌀	sequence_44 listlengths 512 512 ⌀	sequence_45 listlengths 512 512 ⌀	sequence_46 listlengths 512 512 ⌀	sequence_47 listlengths 512 512 ⌀	sequence_48 listlengths 512 512 ⌀	sequence_49 listlengths 512 512 ⌀	sequence_50 listlengths 512 512 ⌀	sequence_51 listlengths 512 512 ⌀	sequence_52 listlengths 512 512 ⌀	sequence_53 listlengths 512 512 ⌀	sequence_54 listlengths 512 512 ⌀	sequence_55 listlengths 512 512 ⌀
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED)	"For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED)	0	Algebra	5	train/algebra/0.json	0	"To ensure that the piecewise function \\( f(x) \\) is continuous, we need to ensure that the left-h(...TRUNCATED)	512	55	11	"{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED)	75	45	0	10	1	['0', '0']	['0', 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"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED)	"For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED)	0	Algebra	5	train/algebra/0.json	0	"To ensure that the piecewise function \\( f(x) \\) is continuous, we need to ensure that the left-h(...TRUNCATED)	512	55	13	"{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED)	75	45	0	10	1	['0', '0']	['0', 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"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED)	"For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. 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"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED)	"For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED)	0	Algebra	5	train/algebra/0.json	0	"To ensure that the piecewise function \\( f(x) \\) is continuous, we need to make sure that the val(...TRUNCATED)	512	102	23	"{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED)	121	91	0	10	1	['0', '0']	['0', '0']	true	[126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,126336,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,5034,126336,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,126336,70685,341,12629,126336,126336,126336,126336,126(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,126336,126336,1(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,297,126336,1263(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,126336,126336,1(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED)	"For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED)	0	Algebra	5	train/algebra/0.json	0	"To ensure that the piecewise function \\( f(x) \\) is continuous, we need to make sure that the val(...TRUNCATED)	512	102	24	"{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED)	121	91	0	10	1	['0', '0']	['0', '0']	true	[126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,126336,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,5034,126336,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,126336,70685,341,12629,126336,126336,126336,126336,126(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,126336,126336,1(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,297,126336,1263(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,126336,126336,1(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED)	"For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED)	0	Algebra	5	train/algebra/0.json	0	"To ensure that the piecewise function \\( f(x) \\) is continuous, we need to make sure that the val(...TRUNCATED)	512	101	25	"{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED)	121	91	0	10	1	['0', '0']	['0', '0']	true	[126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,126336,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,5034,126336,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,126336,70685,341,12629,126336,126336,126336,126336,126(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,126336,126336,1(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,126336,126336,126336,297,126336,1263(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,126336,126336,1(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,1253,2607,378,268,16(...TRUNCATED)
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED)	"For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED)	0	Algebra	5	train/algebra/0.json	0	"To ensure that the piecewise function \\( f(x) \\) is continuous, we need to ensure that the left-h(...TRUNCATED)	512	108	31	"{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED)	118	98	0	10	1	['0', '0']	['0', '0']	true	[126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[126336,5034,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED)	[2088,5034,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,12633(...TRUNCATED)	[2088,5034,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,12633(...TRUNCATED)	[2088,5034,126336,126336,117254,126336,126336,126336,126336,126336,126336,126336,126336,126336,12633(...TRUNCATED)	[2088,5034,378,126336,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED)	[2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,126336,126336,126336,126336,126336,341,126336,126336,126336,126336,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,126336,3698,126336,126336,341,12629,126336,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,126336,3698,126336,70685,341,12629,126336,126336,126336,126336,(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,126336,3698,126336,70685,341,12629,126336,126336,1050,126336,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,126336(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,126336,126336,268,12(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,126336,268,1263(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,126336,(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)	[2088,5034,378,268,117254,1399,24946,281,3698,8,70685,341,12629,11,438,1050,297,5034,378,268,2914,23(...TRUNCATED)
"Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le(...TRUNCATED)	"For the piecewise function to be continuous, the cases must \"meet\" at $2$ and $-2$. For example, (...TRUNCATED)	0	Algebra	5	train/algebra/0.json	0	"To ensure that the piecewise function \\( f(x) \\) is continuous, we need to ensure that the left-h(...TRUNCATED)	512	108	32	"{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED)	118	98	0	10	1	['0', '0']	['0', 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What is the area of the triangle bounded by the lines $y=x,$ $y=-x,$ and $y=6$?	"[asy]\nsize(200); defaultpen(linewidth(0.8));\nxlimits(-8,8); ylimits(-1,10);\nxaxis(Label(\"$x$\")(...TRUNCATED)	36	Geometry	3	train/geometry/218.json	1	"To find the area of the triangle bounded by the lines \\( y = x \\), \\( y = -x \\), and \\( y = 6 (...TRUNCATED)	512	77	31	"{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED)	87	67	0	10	1	['36', '36']	['36', 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Twenty-seven increased by twice a number is 39. What is the number?	"We are asked to solve $27+2x=39$ for $x$. We subtract 27 from both sides and then multiply both si(...TRUNCATED)	6	Prealgebra	1	train/prealgebra/1915.json	2	"To solve the problem, let's denote the unknown number by \\( x \\).\n\nStep 1: TranslateTwenty-seve(...TRUNCATED)	512	17	0	"{\"accumulative_error_tolerance\": 0.2, \"alpha\": 0.86, \"block_length\": 64, \"compute_log_probs\(...TRUNCATED)	23	14	0	3	1	['6', '6']	['6', '6']	true	[126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,1(...TRUNCATED)	[2088,9237,268,3214,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126336,126(...TRUNCATED)	[2088,9237,268,3214,126336,126336,698,126336,126336,126336,126336,126336,126336,126336,126336,126336(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,126336,126336,12(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	[2088,9237,268,3214,11,1993,698,22978,268,12398,1788,527,24946,1529,795,931,198,198,8963,220,16,25,6(...TRUNCATED)	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null	null

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