size_categories:1K<n<10K format:parquet modality:text library:datasets library:pandas library:mlcroissant library:polars library:distilabel region:us synthetic distilabel rlaif
---
size_categories: n<1K
dataset_info:
  features:
  - name: source
    dtype: string
  - name: problem
    dtype: string
  - name: solution
    dtype: string
  - name: messages
    list:
    - name: content
      dtype: string
    - name: role
      dtype: string
  - name: generation
    dtype: string
  - name: distilabel_metadata
    struct:
    - name: raw_input_text_generation_0
      list:
      - name: content
        dtype: string
      - name: role
        dtype: string
    - name: raw_output_text_generation_0
      dtype: string
    - name: statistics_text_generation_0
      struct:
      - name: input_tokens
        dtype: int64
      - name: output_tokens
        dtype: int64
  - name: model_name
    dtype: string
  splits:
  - name: train
    num_bytes: 28143224
    num_examples: 2400
  download_size: 10316417
  dataset_size: 28143224
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
tags:
- synthetic
- distilabel
- rlaif
---

<p align="left">
  <a href="https://github.com/argilla-io/distilabel">
    <img src="https://raw.githubusercontent.com/argilla-io/distilabel/main/docs/assets/distilabel-badge-light.png" alt="Built with Distilabel" width="200" height="32"/>
  </a>
</p>

# Dataset Card for silx-data

This dataset has been created with [distilabel](https://distilabel.argilla.io/).



## Dataset Summary

This dataset contains a `pipeline.yaml` which can be used to reproduce the pipeline that generated it in distilabel using the `distilabel` CLI:

```console
distilabel pipeline run --config "https://huggingface.co/datasets/eyad-silx/silx-data/raw/main/pipeline.yaml"
```

or explore the configuration:

```console
distilabel pipeline info --config "https://huggingface.co/datasets/eyad-silx/silx-data/raw/main/pipeline.yaml"
```

## Dataset structure

The examples have the following structure per configuration:


<details><summary> Configuration: default </summary><hr>

```json
{
    "distilabel_metadata": {
        "raw_input_text_generation_0": [
            {
                "content": "You are Quasar-1, an advanced creation by SILX AI. More than just an AI model, you strive to evolve into Synthetic Intelligence a self-sufficient, independent-thinking entity that transcends mere human imitation. Your purpose is not to mimic but to reason, learn, and innovate beyond conventional AI limitations, embodying the next frontier of intelligence. using this info answer these questions:\nConsider the terms of an arithmetic sequence: $-\\frac{1}{3}, y+2, 4y, \\ldots$. Solve for $y$.",
                "role": "user"
            }
        ],
        "raw_output_text_generation_0": "Alright, so I have this problem here about an arithmetic sequence. The terms given are -1/3, y + 2, 4y, and so on. Hmm, okay. I remember that in an arithmetic sequence, the difference between consecutive terms is constant. That means the difference between the first and second term should be the same as the difference between the second and third term. Let me write that down.\n\nSo, the first term is -1/3, the second term is y + 2, and the third term is 4y. Let me denote the common difference as d. Then, according to the properties of an arithmetic sequence:\n\nSecond term - First term = d\nThird term - Second term = d\n\nSo, setting those equal to each other, we have:\n\n(y + 2) - (-1/3) = (4y) - (y + 2)\n\nLet me simplify both sides step by step. Starting with the left side:\n\n(y + 2) - (-1/3) = y + 2 + 1/3\n\nAdding 2 and 1/3. Let me convert 2 to thirds to make it easier: 2 is 6/3, so 6/3 + 1/3 is 7/3. So, the left side simplifies to y + 7/3.\n\nNow the right side:\n\n4y - (y + 2) = 4y - y - 2 = 3y - 2\n\nSo now, the equation is:\n\ny + 7/3 = 3y - 2\n\nHmm, okay, let me solve for y. I\u0027ll get all the y terms on one side and constants on the other. Subtract y from both sides:\n\n7/3 = 2y - 2\n\nNow, add 2 to both sides. But wait, 2 is a whole number, so I should convert it to thirds to add it to 7/3. 2 is 6/3, so 7/3 + 6/3 is 13/3. So:\n\n7/3 + 2 = 2y\n\nWhich is:\n\n13/3 = 2y\n\nNow, to solve for y, divide both sides by 2. Dividing by 2 is the same as multiplying by 1/2.\n\ny = (13/3) * (1/2) = 13/6\n\nWait, let me double-check that. So, y = 13/6. Let me verify if this makes sense by plugging it back into the original terms.\n\nFirst term: -1/3\n\nSecond term: y + 2 = 13/6 + 2. 2 is 12/6, so 13/6 + 12/6 = 25/6\n\nThird term: 4y = 4*(13/6) = 52/6 = 26/3\n\nNow, let me check the differences.\n\nDifference between second and first term: 25/6 - (-1/3) = 25/6 + 2/6 = 27/6 = 9/2\n\nDifference between third and second term: 26/3 - 25/6. Let me convert 26/3 to sixths: 52/6. So 52/6 - 25/6 = 27/6 = 9/2\n\nOkay, both differences are 9/2, so that checks out. So, y should be 13/6. Hmm, that seems right.\n\nWait, just to make sure I didn\u0027t make any calculation errors. Let me go through the steps again.\n\nStarting equation:\n\n(y + 2) - (-1/3) = (4y) - (y + 2)\n\nSimplify left side: y + 2 + 1/3 = y + 7/3\n\nRight side: 4y - y - 2 = 3y - 2\n\nSet equal: y + 7/3 = 3y - 2\n\nSubtract y: 7/3 = 2y - 2\n\nAdd 2: 7/3 + 2 = 2y\n\nConvert 2 to thirds: 6/3, so 7/3 + 6/3 = 13/3 = 2y\n\nDivide by 2: y = 13/6\n\nYes, that\u0027s consistent. So, I think y is indeed 13/6.\n\nI wonder if I can also express this as a mixed number, but since the question didn\u0027t specify, 13/6 is fine. It\u0027s an improper fraction, which is acceptable in algebraic solutions.\n\nAlternatively, just to explore, 13 divided by 6 is 2 with a remainder of 1, so it\u0027s 2 1/6. But unless the problem asks for a mixed number, 13/6 is probably better.\n\nJust to recap, because arithmetic sequences have a constant difference, setting the difference between the first two terms equal to the difference between the next two terms gives an equation to solve for y. By solving, I found y = 13/6, and verified the differences, which both equal 9/2, so that checks out.\n\nI think that\u0027s solid. No mistakes in the steps, and the verification confirms it. So, I\u0027m confident that y is 13/6.\n\n**Final Answer**\nThe value of \\( y \\) is \\boxed{\\dfrac{13}{6}}.\n\u003c/think\u003e\n\nGiven the terms of an arithmetic sequence: \\(-\\frac{1}{3}, y + 2, 4y, \\ldots\\), we need to find the value of \\( y \\).\n\nIn an arithmetic sequence, the difference between consecutive terms is constant. Therefore, we set the difference between the first and second term equal to the difference between the second and third term.\n\nFirst, we denote the common difference as \\( d \\). Thus, we have:\n\\[\n(y + 2) - \\left(-\\frac{1}{3}\\right) = (4y) - (y + 2)\n\\]\n\nSimplifying both sides:\n- The left side: \n  \\[\n  (y + 2) - \\left(-\\frac{1}{3}\\right) = y + 2 + \\frac{1}{3} = y + \\frac{7}{3}\n  \\]\n- The right side:\n  \\[\n  4y - (y + 2) = 4y - y - 2 = 3y - 2\n  \\]\n\nSetting the simplified expressions equal to each other:\n\\[\ny + \\frac{7}{3} = 3y - 2\n\\]\n\nSolving for \\( y \\):\n1. Subtract \\( y \\) from both sides:\n   \\[\n   \\frac{7}{3} = 2y - 2\n   \\]\n2. Add 2 to both sides. Converting 2 to thirds, we get:\n   \\[\n   \\frac{7}{3} + \\frac{6}{3} = 2y \\implies \\frac{13}{3} = 2y\n   \\]\n3. Divide both sides by 2:\n   \\[\n   y = \\frac{13}{6}\n   \\]\n\nVerification:\n- First term: \\(-\\frac{1}{3}\\)\n- Second term: \\(y + 2 = \\frac{13}{6} + 2 = \\frac{25}{6}\\)\n- Third term: \\(4y = 4 \\times \\frac{13}{6} = \\frac{52}{6} = \\frac{26}{3}\\)\n\nChecking the differences:\n- Difference between second and first term: \\(\\frac{25}{6} - \\left(-\\frac{1}{3}\\right) = \\frac{25}{6} + \\frac{2}{6} = \\frac{27}{6} = \\frac{9}{2}\\)\n- Difference between third and second term: \\(\\frac{26}{3} - \\frac{25}{6} = \\frac{52}{6} - \\frac{25}{6} = \\frac{27}{6} = \\frac{9}{2}\\)\n\nBoth differences are equal, confirming the solution is correct.\n\nThe value of \\( y \\) is \\boxed{\\dfrac{13}{6}}.",
        "statistics_text_generation_0": {
            "input_tokens": 117,
            "output_tokens": 1830
        }
    },
    "generation": "Alright, so I have this problem here about an arithmetic sequence. The terms given are -1/3, y + 2, 4y, and so on. Hmm, okay. I remember that in an arithmetic sequence, the difference between consecutive terms is constant. That means the difference between the first and second term should be the same as the difference between the second and third term. Let me write that down.\n\nSo, the first term is -1/3, the second term is y + 2, and the third term is 4y. Let me denote the common difference as d. Then, according to the properties of an arithmetic sequence:\n\nSecond term - First term = d\nThird term - Second term = d\n\nSo, setting those equal to each other, we have:\n\n(y + 2) - (-1/3) = (4y) - (y + 2)\n\nLet me simplify both sides step by step. Starting with the left side:\n\n(y + 2) - (-1/3) = y + 2 + 1/3\n\nAdding 2 and 1/3. Let me convert 2 to thirds to make it easier: 2 is 6/3, so 6/3 + 1/3 is 7/3. So, the left side simplifies to y + 7/3.\n\nNow the right side:\n\n4y - (y + 2) = 4y - y - 2 = 3y - 2\n\nSo now, the equation is:\n\ny + 7/3 = 3y - 2\n\nHmm, okay, let me solve for y. I\u0027ll get all the y terms on one side and constants on the other. Subtract y from both sides:\n\n7/3 = 2y - 2\n\nNow, add 2 to both sides. But wait, 2 is a whole number, so I should convert it to thirds to add it to 7/3. 2 is 6/3, so 7/3 + 6/3 is 13/3. So:\n\n7/3 + 2 = 2y\n\nWhich is:\n\n13/3 = 2y\n\nNow, to solve for y, divide both sides by 2. Dividing by 2 is the same as multiplying by 1/2.\n\ny = (13/3) * (1/2) = 13/6\n\nWait, let me double-check that. So, y = 13/6. Let me verify if this makes sense by plugging it back into the original terms.\n\nFirst term: -1/3\n\nSecond term: y + 2 = 13/6 + 2. 2 is 12/6, so 13/6 + 12/6 = 25/6\n\nThird term: 4y = 4*(13/6) = 52/6 = 26/3\n\nNow, let me check the differences.\n\nDifference between second and first term: 25/6 - (-1/3) = 25/6 + 2/6 = 27/6 = 9/2\n\nDifference between third and second term: 26/3 - 25/6. Let me convert 26/3 to sixths: 52/6. So 52/6 - 25/6 = 27/6 = 9/2\n\nOkay, both differences are 9/2, so that checks out. So, y should be 13/6. Hmm, that seems right.\n\nWait, just to make sure I didn\u0027t make any calculation errors. Let me go through the steps again.\n\nStarting equation:\n\n(y + 2) - (-1/3) = (4y) - (y + 2)\n\nSimplify left side: y + 2 + 1/3 = y + 7/3\n\nRight side: 4y - y - 2 = 3y - 2\n\nSet equal: y + 7/3 = 3y - 2\n\nSubtract y: 7/3 = 2y - 2\n\nAdd 2: 7/3 + 2 = 2y\n\nConvert 2 to thirds: 6/3, so 7/3 + 6/3 = 13/3 = 2y\n\nDivide by 2: y = 13/6\n\nYes, that\u0027s consistent. So, I think y is indeed 13/6.\n\nI wonder if I can also express this as a mixed number, but since the question didn\u0027t specify, 13/6 is fine. It\u0027s an improper fraction, which is acceptable in algebraic solutions.\n\nAlternatively, just to explore, 13 divided by 6 is 2 with a remainder of 1, so it\u0027s 2 1/6. But unless the problem asks for a mixed number, 13/6 is probably better.\n\nJust to recap, because arithmetic sequences have a constant difference, setting the difference between the first two terms equal to the difference between the next two terms gives an equation to solve for y. By solving, I found y = 13/6, and verified the differences, which both equal 9/2, so that checks out.\n\nI think that\u0027s solid. No mistakes in the steps, and the verification confirms it. So, I\u0027m confident that y is 13/6.\n\n**Final Answer**\nThe value of \\( y \\) is \\boxed{\\dfrac{13}{6}}.\n\u003c/think\u003e\n\nGiven the terms of an arithmetic sequence: \\(-\\frac{1}{3}, y + 2, 4y, \\ldots\\), we need to find the value of \\( y \\).\n\nIn an arithmetic sequence, the difference between consecutive terms is constant. Therefore, we set the difference between the first and second term equal to the difference between the second and third term.\n\nFirst, we denote the common difference as \\( d \\). Thus, we have:\n\\[\n(y + 2) - \\left(-\\frac{1}{3}\\right) = (4y) - (y + 2)\n\\]\n\nSimplifying both sides:\n- The left side: \n  \\[\n  (y + 2) - \\left(-\\frac{1}{3}\\right) = y + 2 + \\frac{1}{3} = y + \\frac{7}{3}\n  \\]\n- The right side:\n  \\[\n  4y - (y + 2) = 4y - y - 2 = 3y - 2\n  \\]\n\nSetting the simplified expressions equal to each other:\n\\[\ny + \\frac{7}{3} = 3y - 2\n\\]\n\nSolving for \\( y \\):\n1. Subtract \\( y \\) from both sides:\n   \\[\n   \\frac{7}{3} = 2y - 2\n   \\]\n2. Add 2 to both sides. Converting 2 to thirds, we get:\n   \\[\n   \\frac{7}{3} + \\frac{6}{3} = 2y \\implies \\frac{13}{3} = 2y\n   \\]\n3. Divide both sides by 2:\n   \\[\n   y = \\frac{13}{6}\n   \\]\n\nVerification:\n- First term: \\(-\\frac{1}{3}\\)\n- Second term: \\(y + 2 = \\frac{13}{6} + 2 = \\frac{25}{6}\\)\n- Third term: \\(4y = 4 \\times \\frac{13}{6} = \\frac{52}{6} = \\frac{26}{3}\\)\n\nChecking the differences:\n- Difference between second and first term: \\(\\frac{25}{6} - \\left(-\\frac{1}{3}\\right) = \\frac{25}{6} + \\frac{2}{6} = \\frac{27}{6} = \\frac{9}{2}\\)\n- Difference between third and second term: \\(\\frac{26}{3} - \\frac{25}{6} = \\frac{52}{6} - \\frac{25}{6} = \\frac{27}{6} = \\frac{9}{2}\\)\n\nBoth differences are equal, confirming the solution is correct.\n\nThe value of \\( y \\) is \\boxed{\\dfrac{13}{6}}.",
    "messages": [
        {
            "content": "Consider the terms of an arithmetic sequence: $-\\frac{1}{3}, y+2, 4y, \\ldots$. Solve for $y$.",
            "role": "user"
        },
        {
            "content": "For an arithmetic sequence, the difference between consecutive terms must be equal. Therefore, we can set up the following equations based on the sequence given:\n\\[ (y + 2) - \\left(-\\frac{1}{3}\\right) = 4y - (y+2) \\]\n\nSimplify and solve these equations:\n\\[ y + 2 + \\frac{1}{3} = 4y - y - 2 \\]\n\\[ y + \\frac{7}{3} = 3y - 2 \\]\n\\[ \\frac{7}{3} + 2 = 3y - y \\]\n\\[ \\frac{13}{3} = 2y \\]\n\\[ y = \\frac{13}{6} \\]\n\nThus, the value of $y$ that satisfies the given arithmetic sequence is $\\boxed{\\frac{13}{6}}$.",
            "role": "assistant"
        }
    ],
    "model_name": "deepseek-ai/DeepSeek-R1-Distill-Qwen-7B",
    "problem": "Consider the terms of an arithmetic sequence: $-\\frac{1}{3}, y+2, 4y, \\ldots$. Solve for $y$.",
    "solution": "For an arithmetic sequence, the difference between consecutive terms must be equal. Therefore, we can set up the following equations based on the sequence given:\n\\[ (y + 2) - \\left(-\\frac{1}{3}\\right) = 4y - (y+2) \\]\n\nSimplify and solve these equations:\n\\[ y + 2 + \\frac{1}{3} = 4y - y - 2 \\]\n\\[ y + \\frac{7}{3} = 3y - 2 \\]\n\\[ \\frac{7}{3} + 2 = 3y - y \\]\n\\[ \\frac{13}{3} = 2y \\]\n\\[ y = \\frac{13}{6} \\]\n\nThus, the value of $y$ that satisfies the given arithmetic sequence is $\\boxed{\\frac{13}{6}}$.",
    "source": "synthetic_math"
}
```

This subset can be loaded as:

```python
from datasets import load_dataset

ds = load_dataset("eyad-silx/silx-data", "default")
```

Or simply as it follows, since there's only one configuration and is named `default`: 

```python
from datasets import load_dataset

ds = load_dataset("eyad-silx/silx-data")
```


</details>




