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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"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 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... | \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 | [
"Rewritten Question: Find the derivative of \\( y = \\sin 3x \\) using the definition of the derivative at \\( x = \\frac{\\pi}{9} \\).\n\nStep 1: Recall the definition of the derivative.\n\\[ f'(x) = \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h} \\]\n\nStep 2: Apply this definition to \\( y = \\sin 3x \\).\n\\[ f(x) =... | [
false
] | [
"\\frac{3}{2}"
] | 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 applied the definition of the derivative, used the appropriate trigonometric identities, and evaluated the limit properly. It also correctly substituted the value \\( x = \\frac{\\pi}{9} \\) and simplified the cosine term. \n\n<verdict>\nCorrect\n</verdict>"
... | [
false
] | [
""
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"api_url": "http://10.32.36.214:9080/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 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 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... | \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 | [
"Rewritten Question: Find the derivative of \\( y = \\sin 3x \\) using the definition of the derivative at \\( x = \\frac{\\pi}{9} \\).\n\nStep 1: Write down the definition of the derivative.\n\\[ f'(x) = \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h} \\]\n\nStep 2: Apply the definition to \\( f(x) = \\sin 3x \\).\n\\[ ... | [
false
] | [
"\\frac{3}{2}"
] | 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 follows the steps required to find the derivative of \\( y = \\sin 3x \\) at \\( x = \\frac{\\pi}{9} \\) using the definition of the derivative. It uses the appropriate trigonometric identities and limits to simplify the expression, ultimately arriving at the... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.214:9080/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 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 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... | \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 | [
"Rewritten Question: Find the derivative of \\( y = \\sin 3x \\) using the definition of the derivative at \\( x = \\pi / 9 \\).\n\nStep 1: Recall the definition of the derivative.\n\\[ f'(x) = \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h} \\]\n\nStep 2: Apply this definition to \\( y = \\sin 3x \\).\n\\[ f(x) = \\sin ... | [
false
] | [
"\\frac{3}{2}"
] | 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 applied the definition of the derivative to the function \\( y = \\sin 3x \\) and arrived at the derivative \\( f'(x) = 3 \\cos 3x \\). Evaluating this derivative at \\( x = \\pi / 9 \\) yielded \\( f'(\\pi / 9) = 3 \\cos (\\pi / 3) = 3 \\cdot 1/2 = 3/2 \\). This matc... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.214:9080/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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | \dfrac{3}{2} | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Find the derivative of \\( y = \\sin 3x \\) using the definition of the deriva(...TRUNCATED) | [
false
] | [
"\\frac{3}{2}"
] | 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 applied the definition of the derivative, used the (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.214:9080/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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...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 \\) at the point \\( x = \\pi/9 \\) using the definitio(...TRUNCATED) | [
false
] | [
"\\frac{3}{2}"
] | 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 applied the definition of the derivative and simpli(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.214:9080/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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...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 \\) at the point \\( x = \\pi/9 \\), we start by recall(...TRUNCATED) | [
false
] | [
"\\frac{3}{2}"
] | 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 applied the definition of the derivative, used the (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.214:9080/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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...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 \\) at the point \\( x = \\pi / 9 \\), we start with th(...TRUNCATED) | [
false
] | [
"\\frac{3}{2}"
] | 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 applied the definition of the derivative, simplifie(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.214:9080/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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...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 \\) at \\( x = \\pi / 9 \\), we start with the definiti(...TRUNCATED) | [
false
] | [
"\\frac{3}{2}"
] | 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 carefully examining the model response. The model starts by correctly(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.214:9080/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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 737 | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: In a right triangle \\(ABC\\) with a right angle at \\(C\\), \\(CA = 30\\) and(...TRUNCATED) | [
true
] | [
"737"
] | 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 response starts off well by calculating the hypotenuse correc(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.214:9080/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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 737 | {"api_url":"http://10.32.36.232:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: In a right triangle \\(ABC\\) with a right angle at \\(C\\), \\(CA = 30\\) and(...TRUNCATED) | [
true
] | [
"737"
] | 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 response starts off well by calculating the hypotenuse using (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.214:9080/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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