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 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"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 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 steps taken in the model response. The model correctly applied the definition of the derivative to find the derivative of \\( y = \\sin(3x) \\) and arrived at \\( f'(x) = 3\\cos(3x) \\). It also correctly evaluated the derivative at \\( x = \\frac{\\pi}{9} \\) and obtained... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.232:10080/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": "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 uses the definition of the derivative and applies the appropriate trigonometric identities and limits to arrive at the derivative of \\(y = \\sin 3x\\), which is \\(3 \\cos 3x\\). Evaluating this derivative at \\(x = \\frac{\\pi}{9}\\) results in \\(3 \\cos \... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.232:10080/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": "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. The model correctly applies the definition of the derivative, uses the angle addition formula for sine, separates the limits, and evaluates them properly. It arrives at the derivative \\(3\\cos(3x)\\) and correctly substitutes \\(x = \\pi/9\\), leading to the value \\(\\frac{3}{2}\\). Th... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.232:10080/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":"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 response correctly applies the definition of the derivative t(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.232:10080/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":"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 checking the steps taken. The response correctly identifies the funct(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.232:10080/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":"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 checking the detailed steps and logic presented in the model response(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.232:10080/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":"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 by reviewing the model's solution process. The model correctly identifie(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.232:10080/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":"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 rechecking the steps. The model has correctly applied the definition (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.232:10080/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":"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 | ["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 response correctly applied the definition of the derivative t(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.232:10080/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":"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 | ["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 by rechecking the main steps. The process involved using the definition (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.232:10080/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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