conversations listlengths 2 2 | question stringlengths 24 1.12k | source null | id null | prompt listlengths 2 2 | answer stringclasses 520
values | prompt__example_annotation__metadata dict | task_source stringclasses 1
value | task_config stringclasses 1
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 2
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": "Among the following functions, the one with the smallest positive period $T=\\pi$ is $(\\quad\\quad)$.\nA: $y=|\\sin x|$\nB: $y=\\tan 2x$\nC: $y=\\cos \\frac {x}{2}$\nD: $y=\\sin x$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is asking w... | Among the following functions, the one with the smallest positive period $T=\pi$ is $(\quad\quad)$.
A: $y=|\sin x|$
B: $y=\tan 2x$
C: $y=\cos \frac {x}{2}$
D: $y=\sin x$ | 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... | A | {
"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: Among the following functions, which has the smallest positive period \\( T = \\pi \\)?\nA: \\( y = |\\sin x| \\)\nB: \\( y = \\tan 2x \\)\nC: \\( y = \\cos \\frac{x}{2} \\)\nD: \\( y = \\sin x \\)\n\nStep 1: Determine the period of each function.\n- For \\( y = \\sin x \\), the period is \\( 2... | [
true
] | [
"A"
] | 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 correctly identified the periods of each function and compared them to find the smallest positive period equal to \\(\\pi\\). It accurately stated that the period of \\(y = \\sin x\\) is \\(2\\pi\\), the period of \\(y = \\tan 2x\\) is \\(\\frac{\\pi}{2}\\), the period of \\(y ... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:10080/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": "Among the following functions, the one with the smallest positive period $T=\\pi$ is $(\\quad\\quad)$.\nA: $y=|\\sin x|$\nB: $y=\\tan 2x$\nC: $y=\\cos \\frac {x}{2}$\nD: $y=\\sin x$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is asking w... | Among the following functions, the one with the smallest positive period $T=\pi$ is $(\quad\quad)$.
A: $y=|\sin x|$
B: $y=\tan 2x$
C: $y=\cos \frac {x}{2}$
D: $y=\sin x$ | 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... | A | {
"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 | [
"To determine which function has the smallest positive period \\( T = \\pi \\), we need to analyze the periodicity of each given function.\n\n**Option A: \\( y = |\\sin x| \\)**\nThe function \\( \\sin x \\) has a period of \\( 2\\pi \\). Taking the absolute value of \\( \\sin x \\) results in a function where ever... | [
true
] | [
"A"
] | alternative_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 correctly identified the periods of each function:\n\n- For \\( y = |\\sin x| \\), the period is indeed \\( \\pi \\).\n- For \\( y = \\tan 2x \\), the period is \\( \\frac{\\pi}{2} \\).\n- For \\( y = \\cos \\frac{x}{2} \\), the period is \\( 4\\pi \\).\n- For \\( y = \\sin x \... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:10080/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": "Among the following functions, the one with the smallest positive period $T=\\pi$ is $(\\quad\\quad)$.\nA: $y=|\\sin x|$\nB: $y=\\tan 2x$\nC: $y=\\cos \\frac {x}{2}$\nD: $y=\\sin x$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is asking w... | Among the following functions, the one with the smallest positive period $T=\pi$ is $(\quad\quad)$.
A: $y=|\sin x|$
B: $y=\tan 2x$
C: $y=\cos \frac {x}{2}$
D: $y=\sin x$ | 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... | A | {
"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 | [
"To determine which function among the given options has the smallest positive period \\( T = \\pi \\), we need to analyze the periodicity of each function individually.\n\n**Option A: \\( y = |\\sin x| \\)**\n- The sine function \\( \\sin x \\) has a period of \\( 2\\pi \\).\n- Taking the absolute value of \\( \\s... | [
true
] | [
"A"
] | alternative_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 correctly identified the periods of each function. It stated that the period of \\( y = |\\sin x| \\) is \\( \\pi \\), while the periods of \\( y = \\tan 2x \\), \\( y = \\cos \\frac{x}{2} \\), and \\( y = \\sin x \\) are \\( \\frac{\\pi}{2} \\), \\( 4\\pi \\), and \\( 2\\pi \\... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:10080/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": "Among the following functions, the one with the smallest positive period $T=\\pi$ is $(\\quad\\quad)$.\nA: $y=|\\sin x|$\nB: $y=\\tan 2x$\nC: $y=\\cos \\frac {x}{2}$\nD: $y=\\sin x$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is asking w... | Among the following functions, the one with the smallest positive period $T=\pi$ is $(\quad\quad)$.
A: $y=|\sin x|$
B: $y=\tan 2x$
C: $y=\cos \frac {x}{2}$
D: $y=\sin x$ | 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... | A | {
"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 | [
"To determine which function among the given options has the smallest positive period \\( T = \\pi \\), let's analyze each option step by step.\n\n**Option A: \\( y = |\\sin x| \\)**\n\n1. The basic sine function \\( \\sin x \\) has a period of \\( 2\\pi \\).\n2. Taking the absolute value of \\( \\sin x \\) means w... | [
true
] | [
"A"
] | alternative_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 correctly identifies the periods of each function:\n\n- For \\( y = |\\sin x| \\), the period is \\( \\pi \\).\n- For \\( y = \\tan 2x \\), the period is \\( \\frac{\\pi}{2} \\).\n- For \\( y = \\cos \\frac{x}{2} \\), the period is \\( 4\\pi \\).\n- For \\( y = \\sin x \\), the... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:10080/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":"Among the following functions, the one with the smallest positive period $T(...TRUNCATED) | "Among the following functions, the one with the smallest positive period $T=\\pi$ is $(\\quad\\quad(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | A | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To determine which function among the given options has the smallest positive period \\( T = \\pi (...TRUNCATED) | [
true
] | [
"A"
] | 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 each function to determine their periods:\(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:10080/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":"Let set $A = \\{0, 1, 2\\}$, and $B = \\{x \\in \\mathbb{R} | (x+1)(x+2) < (...TRUNCATED) | "Let set $A = \\{0, 1, 2\\}$, and $B = \\{x \\in \\mathbb{R} | (x+1)(x+2) < 0\\}$. The number of ele(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | A | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Let set \\( A = \\{0, 1, 2\\} \\), and \\( B = \\{x \\in \\mathbb{R} | (x+1)(x(...TRUNCATED) | [
true
] | [
"A"
] | 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 rewritten question correctly identifies the task as finding the num(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:10080/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":"Let set $A = \\{0, 1, 2\\}$, and $B = \\{x \\in \\mathbb{R} | (x+1)(x+2) < (...TRUNCATED) | "Let set $A = \\{0, 1, 2\\}$, and $B = \\{x \\in \\mathbb{R} | (x+1)(x+2) < 0\\}$. The number of ele(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | A | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Let set \\(A = \\{0, 1, 2\\}\\), and \\(B = \\{x \\in \\mathbb{R} | (x+1)(x+2)(...TRUNCATED) | [
true
] | [
"A"
] | 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 rewritten question and steps taken to solve it were accurate. We co(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:10080/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":"Let set $A = \\{0, 1, 2\\}$, and $B = \\{x \\in \\mathbb{R} | (x+1)(x+2) < (...TRUNCATED) | "Let set $A = \\{0, 1, 2\\}$, and $B = \\{x \\in \\mathbb{R} | (x+1)(x+2) < 0\\}$. The number of ele(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | A | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Let set \\( A = \\{0, 1, 2\\} \\), and \\( B = \\{x \\in \\mathbb{R} | (x+1)(x(...TRUNCATED) | [
true
] | [
"A"
] | 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 the interval for set \\( B \\) as \\( (-(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:10080/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":"Let set $A = \\{0, 1, 2\\}$, and $B = \\{x \\in \\mathbb{R} | (x+1)(x+2) < (...TRUNCATED) | "Let set $A = \\{0, 1, 2\\}$, and $B = \\{x \\in \\mathbb{R} | (x+1)(x+2) < 0\\}$. The number of ele(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | A | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Let set \\(A = \\{0, 1, 2\\}\\), and \\(B = \\{x \\in \\mathbb{R} | (x+1)(x+2)(...TRUNCATED) | [
true
] | [
"A"
] | 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 rewritten question correctly identifies the steps required to solve(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:10080/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":"Let set $A = \\{0, 1, 2\\}$, and $B = \\{x \\in \\mathbb{R} | (x+1)(x+2) < (...TRUNCATED) | "Let set $A = \\{0, 1, 2\\}$, and $B = \\{x \\in \\mathbb{R} | (x+1)(x+2) < 0\\}$. The number of ele(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | A | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To determine the number of elements in \\(A \\cap B\\), we first need to identify what sets \\(A\\(...TRUNCATED) | [
true
] | [
"A"
] | 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 by checking if the steps taken in the model response were accurate.\n\n1(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:10080/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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