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values | reflection_prompt listlengths 2 2 | model_responses__mutated_prompts_reflection listlengths 1 1 | model_responses__mutated_prompts_reflection__finish_reason_length_flags listlengths 1 1 | model_responses__mutated_prompts_reflection__length_partial_responses listlengths 1 1 | reflection_prompt__mutated_prompts_reflection__metadata dict | model_responses__mutated_prompts_reflection__metadata dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "user",
"value": "Let $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$, where $a_{1}=1$ and $a_{n+1}=2a_{n}+n-1$. Find $S_{10}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find S₁₀, which is the sum of the first 10 terms of the sequence {aₙ}, wh... | Let $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$, where $a_{1}=1$ and $a_{n+1}=2a_{n}+n-1$. Find $S_{10}$. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 1991 | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"Rewritten Question: Given $a_1 = 1$ and $a_{n+1} = 2a_n + n - 1$, find $S_{10}$.\n\nStep 1: Calculate the first few terms of the sequence.\n- For $n=1$: $a_2 = 2a_1 + 1 - 1 = 2 \\cdot 1 = 2$\n- For $n=2$: $a_3 = 2a_2 + 2 - 1 = 2 \\cdot 2 + 1 = 5$\n- For $n=3$: $a_4 = 2a_3 + 3 - 1 = 2 \\cdot 5 + 2 = 12$\n\nStep 2: ... | [
true
] | [
"1991"
] | rephrase | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer... The model correctly identified the task and provided a detailed step-by-step process to calculate the terms of the sequence and their sum. It correctly derived the closed-form expression \\(a_n = 2^n - n\\) and used it to compute \\(S_{10}\\). The calculations were accurate and followe... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.207:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "Let $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$, where $a_{1}=1$ and $a_{n+1}=2a_{n}+n-1$. Find $S_{10}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find S₁₀, which is the sum of the first 10 terms of the sequence {aₙ}, wh... | Let $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$, where $a_{1}=1$ and $a_{n+1}=2a_{n}+n-1$. Find $S_{10}$. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 1991 | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"To find \\( S_{10} \\), we need to determine the first 10 terms of the sequence \\( \\{a_n\\} \\) defined by \\( a_1 = 1 \\) and \\( a_{n+1} = 2a_n + n - 1 \\). Let's calculate these terms step-by-step.\n\n**Step 1: Calculate the first few terms**\n\nStarting with \\( a_1 = 1 \\):\n\\[ a_2 = 2a_1 + 1 - 1 = 2 \\cdo... | [
true
] | [
"1991"
] | alternative | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer... The model correctly derived the closed-form expression for \\(a_n = 2^n - n\\) and used it to compute \\(S_{10}\\). The calculations provided are detailed and accurate, showing the correct summation steps. The final answer of 1991 is indeed correct based on the derived formula and comp... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.207:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "Let $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$, where $a_{1}=1$ and $a_{n+1}=2a_{n}+n-1$. Find $S_{10}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find S₁₀, which is the sum of the first 10 terms of the sequence {aₙ}, wh... | Let $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$, where $a_{1}=1$ and $a_{n+1}=2a_{n}+n-1$. Find $S_{10}$. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 1991 | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"To find \\( S_{10} \\), we start by understanding the recursive definition of the sequence \\( \\{a_n\\} \\) given by \\( a_1 = 1 \\) and \\( a_{n+1} = 2a_n + n - 1 \\).\n\n**Step 1: Calculate the first few terms manually**\n\nWe can calculate the initial terms to understand the pattern:\n\\[ a_1 = 1 \\]\n\\[ a_2 ... | [
true
] | [
"1991"
] | alternative | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer... The model correctly derived the closed-form expression for \\(a_n = 2^n - n\\) and used it to compute \\(S_{10}\\). The calculations provided were accurate, leading to the correct sum of 1991.\n\n<verdict>\nCorrect\n</verdict>"
] | [
false
] | [
""
] | {
"api_url": "http://10.32.36.207:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given $a \\in \\mathbb{R}$, let set $A = \\{x | x^2 \\neq 1\\}$ and set $B (...TRUNCATED) | "Given $a \\in \\mathbb{R}$, let set $A = \\{x | x^2 \\neq 1\\}$ and set $B = \\{x | ax = 1\\}$. If (...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | D | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Given sets \\( A = \\{x | x^2 \\neq 1\\} \\) and \\( B = \\{x | ax = 1\\} \\),(...TRUNCATED) | [
false
] | [
"D: -1, 0, or 1"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer... The rewritten question and the model response correctly identify that(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given $a \\in \\mathbb{R}$, let set $A = \\{x | x^2 \\neq 1\\}$ and set $B (...TRUNCATED) | "Given $a \\in \\mathbb{R}$, let set $A = \\{x | x^2 \\neq 1\\}$ and set $B = \\{x | ax = 1\\}$. If (...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | D | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Given sets \\(A = \\{x | x^2 \\neq 1\\}\\) and \\(B = \\{x | ax = 1\\}\\), if (...TRUNCATED) | [
false
] | [
"D: -1, 0, or 1"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer... The rewritten question and the model response correctly identify the (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given $a \\in \\mathbb{R}$, let set $A = \\{x | x^2 \\neq 1\\}$ and set $B (...TRUNCATED) | "Given $a \\in \\mathbb{R}$, let set $A = \\{x | x^2 \\neq 1\\}$ and set $B = \\{x | ax = 1\\}$. If (...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | D | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve this problem, we need to understand the sets \\(A\\) and \\(B\\) and how their union rela(...TRUNCATED) | [
false
] | [
"D: -1, 0, or 1"
] | alternative | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer... The model correctly identified that the union of sets \\(A\\) and \\((...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given $a \\in \\mathbb{R}$, let set $A = \\{x | x^2 \\neq 1\\}$ and set $B (...TRUNCATED) | "Given $a \\in \\mathbb{R}$, let set $A = \\{x | x^2 \\neq 1\\}$ and set $B = \\{x | ax = 1\\}$. If (...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | D | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To solve this problem, we need to analyze the given sets \\( A \\) and \\( B \\), and use the cond(...TRUNCATED) | [
false
] | [
"D: -1, 0, or 1"
] | alternative | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer... The model correctly identified that the union of sets \\(A\\) and \\((...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"In a college entrance mathematics examination, there are three optional pro(...TRUNCATED) | "In a college entrance mathematics examination, there are three optional problems, and each student (...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | \dfrac{1}{3} | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Two students independently choose one out of three problems. What is the proba(...TRUNCATED) | [
false
] | [
"\\frac{1}{3}"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model correctly identified that there are 9 total possible outcomes(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"In a college entrance mathematics examination, there are three optional pro(...TRUNCATED) | "In a college entrance mathematics examination, there are three optional problems, and each student (...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | \dfrac{1}{3} | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Two students, A and B, each choose one out of three problems randomly. What is(...TRUNCATED) | [
false
] | [
"(3/9) which simplifies to 1/3"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model response correctly calculates the total number of possible ou(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"In a college entrance mathematics examination, there are three optional pro(...TRUNCATED) | "In a college entrance mathematics examination, there are three optional problems, and each student (...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | \dfrac{1}{3} | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To determine the probability that both students A and B choose the same problem from the three ava(...TRUNCATED) | [
false
] | [
"\\frac{1}{3}"
] | alternative | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model response correctly calculates the probability by both direct (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
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