conversations listlengths 2 2 | question stringclasses 4
values | source stringclasses 1
value | id int64 11.7k 11.7k ⌀ | prompt listlengths 2 2 | answer stringclasses 4
values | prompt__example_annotation__metadata dict | task_source stringclasses 1
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value | model_responses__example_annotation listlengths 1 1 | model_responses__example_annotation__eval_is_correct listlengths 1 1 | model_responses__example_annotation__eval_extracted_answers listlengths 1 1 | prompt_type stringclasses 4
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 |
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[
{
"from": "user",
"value": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try ... | $2 \cdot 131$ The number of roots of the equation $\sqrt{x^{2}+12 x+36}+x+6=0$ is
(A) 0.
(B) 2.
(C) 4.
(D) Infinitely many.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991) | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | D | {
"api_url": "http://10.32.36.231:9080/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 | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Step-by-Step Plan\n\n1. **Rewrite the Equation**: Start by rewriting the given equation for clarity:\n \\[\n \\sqrt{x^2 + 12x + 36} + x + 6 = 0\n \\]\n\n2. **Simplify th... | [
true
] | [
"D"
] | plan_and_execute_rationalized | [
{
"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 response correctly analyzes the equation and identifies that the solutions include \\(x = -6\\) and all \\(x < -6\\), leading to infinitely many solutions. Given the options provided (A) 0, (B) 2, (C) 4, (D) Infinitely many, the correct choice is indeed D.\n\n<verdict>\nCorrect... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.239:10080/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_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try ... | $2 \cdot 131$ The number of roots of the equation $\sqrt{x^{2}+12 x+36}+x+6=0$ is
(A) 0.
(B) 2.
(C) 4.
(D) Infinitely many.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991) | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | D | {
"api_url": "http://10.32.36.231:9080/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 | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Step-by-Step Plan\n\n1. **Rewrite the Equation**: Start by rewriting the given equation for clarity:\n \\[\n \\sqrt{x^2 + 12x + 36} + x + 6 = 0\n \\]\n\n2. **Simplify In... | [
true
] | [
"D"
] | plan_and_execute_rationalized | [
{
"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 by carefully re-examining the steps taken in the model response.\n\n1. The equation is correctly simplified to \\( |x + 6| + x + 6 = 0 \\).\n2. Two cases are considered:\n - Case 1: \\( x + 6 \\geq 0 \\)\n - Case 2: \\( x + 6 < 0 \\)\n\nFor Case 1, solving \\( (x + 6) + x + 6 = 0 \\) ... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.239:10080/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_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try ... | $2 \cdot 131$ The number of roots of the equation $\sqrt{x^{2}+12 x+36}+x+6=0$ is
(A) 0.
(B) 2.
(C) 4.
(D) Infinitely many.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991) | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | D | {
"api_url": "http://10.32.36.231:9080/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: Find the number of real roots for the equation $\\sqrt{x^2 + 12x + 36} + x + 6 = 0$.\n\nStep 1: Simplify the expression under the square root. Notice that $x^2 + 12x + 36 = (x + 6)^2$. So, the equation becomes $\\sqrt{(x + 6)^2} + x + 6 = 0$.\n\nStep 2: Recognize that $\\sqrt{(x + 6)^2}$ simpli... | [
false
] | [
"(D)"
] | rephrase_rationalized | [
{
"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 response correctly identifies the need to consider two cases based on the absolute value function. It correctly solves for the first case, finding \\(x = -6\\). For the second case, it correctly notes that the equation holds true for any \\(x < -6\\), indicating infinitely many... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.239:10080/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_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x(...TRUNCATED) | "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | D | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Find the number of roots for the equation $\\sqrt{x^2 + 12x + 36} + x + 6 = 0$(...TRUNCATED) | [
true
] | [
"D"
] | rephrase_rationalized | [{"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 equation simplifies to \\(|x + (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.239:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x(...TRUNCATED) | "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | D | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's analyze the given equation step-by-step:\n\nThe equation is:\n\\[\n\\sqrt{x^2 + 12x + 36} + (...TRUNCATED) | [
true
] | [
"D"
] | alternative_rationalized | [{"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 analyzed the equation and broke down the absolute v(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.239:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's analyze each proposition one by one:\n\n**Proposition A:** If \\( |\\overrightarrow{a}| > |\(...TRUNCATED) | [
true
] | [
"B"
] | original_rationalized | [{"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 identifies that Proposition B is the correct choice(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.239:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's analyze each proposition one by one:\n\n**Proposition A:** If \\( |\\overrightarrow{a}| > |\(...TRUNCATED) | [
true
] | [
"B"
] | original_rationalized | [{"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 analyzed each proposition, providing valid reasons (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.239:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's analyze each proposition one by one:\n\n**Proposition A:** If \\( |\\overrightarrow{a}| > |\(...TRUNCATED) | [
true
] | [
"B"
] | original_rationalized | [{"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 Proposition B as the correct proposition(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.239:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's analyze each proposition one by one:\n\n**Proposition A:** If \\(|\\overrightarrow{a}| > |\\(...TRUNCATED) | [
true
] | [
"B"
] | original_rationalized | [{"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 identifies that Proposition A is incorrect due to t(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.239:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["First, I'll try to understand the problem better by writing out a plan and go really deep into det(...TRUNCATED) | [
false
] | [
"(B)"
] | plan_and_execute_rationalized | [{"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 Proposition B is the correct choice(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.239:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
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