solution: The rectangular region is 10 units by 8 units, resulting in an 8 by 6 rectangular region in the interior, which forms a 9-by-7 array of lattice points. That's $\boxed{63}$ points with integer coordinates, as shown in the figure. [asy]
  import olympiad; size(150); defaultpen(linewidth(0.8));
  add(grid(10,8));
  draw((1,1)--(9,1)--(9,7)--(1,7)--cycle,linewidth(1.2));
  [/asy] Note: We are counting points, not squares. It is a common mistake to count the interior squares, for 48, instead of interior lattice points, which gives the correct answer of 63.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Consider the rectangular region with the following points as vertices: $$(5,4), (-5,4), (-5,-4), (5,-4).$$ How many points with integer coordinates will be strictly in the interior of this rectangular region?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 63
extra_info.question: Consider the rectangular region with the following points as vertices: $$(5,4), (-5,4), (-5,-4), (5,-4).$$ How many points with integer coordinates will be strictly in the interior of this rectangular region?
extra_info.split: test