conversations listlengths 2 2 | question stringclasses 4
values | source stringclasses 1
value | id int64 36.4k 36.4k ⌀ | prompt listlengths 2 2 | answer stringclasses 5
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 |
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[
{
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"value": "186. Using the definition of the derivative, find the derivative of the function $y=\\sin 3x$ at the point $x=\\pi / 9$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the derivative of the function y = sin(3x) at the point x = π/9 using the def... | 186. Using the definition of the derivative, find the derivative of the function $y=\sin 3x$ at the point $x=\pi / 9$. | 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... | \dfrac{3}{2} | {
"api_url": "http://10.32.36.232:9080/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 the derivative of \\( y = \\sin(3x) \\) using the definition of the derivative, we start with the limit definition:\n\n\\[ f'(x) = \\lim_{h \\to 0} \\frac{\\sin(3(x + h)) - \\sin(3x)}{h} \\]\n\nFirst, let's simplify the expression inside the limit:\n\n\\[ \\sin(3(x + h)) = \\sin(3x + 3h) \\]\n\nUsing the s... | [
false
] | [
"(3/2)"
] | original_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 checking the calculations and logic presented in the model response. The model correctly applies the definition of the derivative and uses trigonometric identities appropriately. It also correctly evaluates the limits involved. Finally, it arrives at the correct derivative \\( f'(x) = ... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.223:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
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"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": "186. Using the definition of the derivative, find the derivative of the function $y=\\sin 3x$ at the point $x=\\pi / 9$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the derivative of the function y = sin(3x) at the point x = π/9 using the def... | 186. Using the definition of the derivative, find the derivative of the function $y=\sin 3x$ at the point $x=\pi / 9$. | 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... | \dfrac{3}{2} | {
"api_url": "http://10.32.36.232:9080/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 the derivative of \\( y = \\sin 3x \\) using the definition of the derivative, we start from the limit definition:\n\n\\[\nf'(x) = \\lim_{h \\to 0} \\frac{\\sin(3(x + h)) - \\sin(3x)}{h}\n\\]\n\nUsing the angle addition formula for sine, we have:\n\n\\[\n\\sin(3(x + h)) = \\sin(3x + 3h) = \\sin 3x \\cos 3h... | [
false
] | [
"\\frac{3}{2}"
] | original_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 applies the definition of the derivative to the function \\( y = \\sin 3x \\) and arrives at the derivative \\( f'(x) = 3 \\cos 3x \\). Evaluating this derivative at \\( x = \\frac{\\pi}{9} \\) results in \\( f'\\left( \\frac{\\pi}{9} \\right) = 3 \\cos \\lef... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.223:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
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"chat_template_applied": true,
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"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": "186. Using the definition of the derivative, find the derivative of the function $y=\\sin 3x$ at the point $x=\\pi / 9$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the derivative of the function y = sin(3x) at the point x = π/9 using the def... | 186. Using the definition of the derivative, find the derivative of the function $y=\sin 3x$ at the point $x=\pi / 9$. | 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... | \dfrac{3}{2} | {
"api_url": "http://10.32.36.232:9080/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 the derivative of \\( y = \\sin(3x) \\) using the definition of the derivative, we start from the limit definition:\n\n\\[ f'(x) = \\lim_{h \\to 0} \\frac{\\sin(3(x+h)) - \\sin(3x)}{h} \\]\n\nUsing the angle addition formula for sine, we have:\n\n\\[ \\sin(3(x + h)) = \\sin(3x + 3h) = \\sin(3x)\\cos(3h) + ... | [
false
] | [
"\\frac{3}{2}"
] | original_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 checking the mathematical steps taken. The model correctly applied the definition of the derivative, used the angle addition formulas, and evaluated the appropriate limits. The final step of evaluating the derivative at \\(x = \\pi/9\\) also appears accurate. Given the detailed and cor... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.223:9080/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":"186. Using the definition of the derivative, find the derivative of the fun(...TRUNCATED) | "186. Using the definition of the derivative, find the derivative of the function $y=\\sin 3x$ at th(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | \dfrac{3}{2} | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To find the derivative of \\( y = \\sin 3x \\) using the definition of the derivative, we start fr(...TRUNCATED) | [
false
] | [
"\\frac{3}{2}"
] | 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 applied the definition of the derivative and used t(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.223:9080/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":"186. Using the definition of the derivative, find the derivative of the fun(...TRUNCATED) | "186. Using the definition of the derivative, find the derivative of the function $y=\\sin 3x$ at th(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | \dfrac{3}{2} | {"api_url":"http://10.32.36.232:9080/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
] | [
"\\frac{3}{2}"
] | 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 by reviewing the model's solution step by step. The model correctly appl(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.223:9080/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":"186. Using the definition of the derivative, find the derivative of the fun(...TRUNCATED) | "186. Using the definition of the derivative, find the derivative of the function $y=\\sin 3x$ at th(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | \dfrac{3}{2} | {"api_url":"http://10.32.36.232:9080/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
] | [
"\\frac{3}{2}"
] | 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 response walks through the process of finding the derivative (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.223:9080/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":"186. Using the definition of the derivative, find the derivative of the fun(...TRUNCATED) | "186. Using the definition of the derivative, find the derivative of the function $y=\\sin 3x$ at th(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | \dfrac{3}{2} | {"api_url":"http://10.32.36.232:9080/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
] | [
"(3/2)"
] | 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 response provides a detailed derivation of the derivative of (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.223:9080/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":"186. Using the definition of the derivative, find the derivative of the fun(...TRUNCATED) | "186. Using the definition of the derivative, find the derivative of the function $y=\\sin 3x$ at th(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | \dfrac{3}{2} | {"api_url":"http://10.32.36.232:9080/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
] | [
"\\frac{3}{2}"
] | 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 by carefully checking the steps taken in the model response. The model s(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.223:9080/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 [right triangle](https://artofproblemsolving.com/wiki/index.php/Right_tr(...TRUNCATED) | "In [right triangle](https://artofproblemsolving.com/wiki/index.php/Right_triangle) $ABC$ with [righ(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | 737 | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To find the radius \\( r \\) of the circles centered at \\( O_1 \\) and \\( O_2 \\), we start by i(...TRUNCATED) | [
true
] | [
"737"
] | 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 response calculates the radius \\( r \\) of the circles and f(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.223:9080/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 [right triangle](https://artofproblemsolving.com/wiki/index.php/Right_tr(...TRUNCATED) | "In [right triangle](https://artofproblemsolving.com/wiki/index.php/Right_triangle) $ABC$ with [righ(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | 737 | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To find the radius \\( r \\) of the circles, we start by determining the length of the hypotenuse (...TRUNCATED) | [
true
] | [
"737"
] | 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 response calculates the radius of the circles and arrives at (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.223:9080/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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