Datasets:

harman
/

ultrainteract_rrm_50subsamples_filtered0p2thresh_v2_200000

prompt stringlengths 66 14k	chosen listlengths 2 2	rejected listlengths 2 2	neutral bool 2 classes	prob_A float64 0 1
Solve the following math problem step-by-step. Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}. Two points $A(x_1, y_1)$ and $B(x_2, y_2)$ are chosen on the graph of $f(x) = \ln x$, with $0 < x_1 < x_2$. The points $C$ and $D$ trisect $\overline{AB}$, with $AC < CB$. Through $...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTwo points $A(x_1, y_1)$ and $B(x_2, y_2)$ are chosen on the graph of $f(x) = \\ln x$, with $0 < x_1 < x_2$. The points $C$ and $D$ trisect $\\overline{AB}$...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nTwo points $A(x_1, y_1)$ and $B(x_2, y_2)$ are chosen on the graph of $f(x) = \\ln x$, with $0 < x_1 < x_2$. The points $C$ and $D$ trisect $\\overline{AB}$...	true	0.976563
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. a football player scores 4 goals in his fifth match thus increasing hi...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\na football player scores 4 goals in his fif...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\na football player scores 4 goals in his fif...	true	0.992188
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. find the area of the quadrilateral of one of its diagonals is 24 cm an...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nfind the area of the quadrilateral of one o...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nfind the area of the quadrilateral of one o...	true	1
Solve the following problem step-by-step: Given the context and corresponding question, choose the correct answer from the options. Context: Since the deregulation of airlines, delays at the nation' s increasingly busy airports have increased by 25 percent. To combat this problem, more of the takeoff and landing slot...	[ { "content": "Solve the following problem step-by-step:\nGiven the context and corresponding question, choose the correct answer from the options.\n\nContext: \nSince the deregulation of airlines, delays at the nation' s increasingly busy airports have increased by 25 percent. To combat this problem, more of th...	[ { "content": "Solve the following problem step-by-step:\nGiven the context and corresponding question, choose the correct answer from the options.\n\nContext: \nSince the deregulation of airlines, delays at the nation' s increasingly busy airports have increased by 25 percent. To combat this problem, more of th...	true	0.121582
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. Bryan has some 3 cent stamps and some 4 cent stamps. What is the least...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nBryan has some 3 cent stamps and some 4 cen...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nBryan has some 3 cent stamps and some 4 cen...	true	0.263672
Solve the following problem step-by-step: Given the context and corresponding question, choose the correct answer from the options. Context: Mark: The decongestant drug Zokaz was discontinued by its manufacturer because long-term studies revealed that it increased the risk of heart attack. Qualzan, another decongesta...	[ { "content": "Solve the following problem step-by-step:\nGiven the context and corresponding question, choose the correct answer from the options.\n\nContext: \nMark: The decongestant drug Zokaz was discontinued by its manufacturer because long-term studies revealed that it increased the risk of heart attack. Q...	[ { "content": "Solve the following problem step-by-step:\nGiven the context and corresponding question, choose the correct answer from the options.\n\nContext: \nMark: The decongestant drug Zokaz was discontinued by its manufacturer because long-term studies revealed that it increased the risk of heart attack. Q...	false	0.457031
Solve the following math problem step-by-step. Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}. a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 30 % by volume and the capa...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\na tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 30...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\na tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 30...	true	1
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. if x is a sum of all even integers on the interval 13 . . . 61 and y i...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nif x is a sum of all even integers on the i...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nif x is a sum of all even integers on the i...	true	0.988281
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. Find the number of moles of Water formed on combining 3 moles of Metha...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nFind the number of moles of Water formed on...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nFind the number of moles of Water formed on...	false	0.235352
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. In how many ways can 6 distinct beads be placed on a bracelet? (Note t...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nIn how many ways can 6 distinct beads be pl...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nIn how many ways can 6 distinct beads be pl...	true	0.255859
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. Tyler has $100. If he buys 8 scissors for $x each and 10 erasers for $...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nTyler has $100. If he buys 8 scissors for $...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nTyler has $100. If he buys 8 scissors for $...	true	0.863281
Write Python code to solve the task: Shubham has a binary string $s$. A binary string is a string containing only characters "0" and "1". He can perform the following operation on the string any amount of times: Select an index of the string, and flip the character at that index. This means, if the character was "0"...	[ { "content": "Write Python code to solve the task:\nShubham has a binary string $s$. A binary string is a string containing only characters \"0\" and \"1\".\n\nHe can perform the following operation on the string any amount of times: Select an index of the string, and flip the character at that index. This me...	[ { "content": "Write Python code to solve the task:\nShubham has a binary string $s$. A binary string is a string containing only characters \"0\" and \"1\".\n\nHe can perform the following operation on the string any amount of times: Select an index of the string, and flip the character at that index. This me...	true	1
Write Python code to solve the task: # Definition _Balanced number_ is the number that * _The sum of_ all digits to the _left of the middle_ digit(s) and the sum of all digits to the _right of the middle_ digit(s) are _equal_. ____ # Task _Given_* a number, *_Find if it is Balanced or not_...	[ { "content": "Write Python code to solve the task:\n# Definition\n\n_Balanced number_ is the number that * _The sum of_ all digits to the _left of the middle_ digit(s) and the sum of all digits to the _right of the middle_ digit(s) are _equal_.\n\n____\n\n# Task\n\n_Given_* a number, **_...	[ { "content": "Write Python code to solve the task:\n# Definition\n\n_Balanced number_ is the number that * _The sum of_ all digits to the _left of the middle_ digit(s) and the sum of all digits to the _right of the middle_ digit(s) are _equal_.\n\n____\n\n# Task\n\n_Given_* a number, **_...	false	0.28125
Solve the following math problem step-by-step. Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}. A four-digit integer $m$ and the four-digit integer obtained by reversing the order of the digits of $m$ are both divisible by 45. If $m$ is divisible by 7, what is the greatest pos...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA four-digit integer $m$ and the four-digit integer obtained by reversing the order of the digits of $m$ are both divisible by 45. If $m$ is divisible by 7,...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA four-digit integer $m$ and the four-digit integer obtained by reversing the order of the digits of $m$ are both divisible by 45. If $m$ is divisible by 7,...	true	1
Write Python code to solve the task: Dilku and Bhopu live in Artland. Dilku loves Bhopu and he writes a message : “iloveyou” on paper and wishes to send it to Bhopu. As Dilku is busy making an artwork, he asks his friend Raj to send the message to Bhopu. However Raj has a condition that he may add/remove some charact...	[ { "content": "Write Python code to solve the task:\nDilku and Bhopu live in Artland. Dilku loves Bhopu and he writes a message : \n“iloveyou”\non paper and wishes to send it to Bhopu. As Dilku is busy making an artwork, he asks his friend Raj to send the message to Bhopu. However Raj has a condition that he may...	[ { "content": "Write Python code to solve the task:\nDilku and Bhopu live in Artland. Dilku loves Bhopu and he writes a message : \n“iloveyou”\non paper and wishes to send it to Bhopu. As Dilku is busy making an artwork, he asks his friend Raj to send the message to Bhopu. However Raj has a condition that he may...	true	0.117676
Solve the following math problem step-by-step. Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}. The average age of five children is 6 years old. Each child is a different age and there is a difference of two years in the ages of any two consecutive children. In years, how old ...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe average age of five children is 6 years old. Each child is a different age and there is a difference of two years in the ages of any two consecutive chi...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nThe average age of five children is 6 years old. Each child is a different age and there is a difference of two years in the ages of any two consecutive chi...	true	1
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. The equation $x^2-kx-12=0$ has only integer solutions for certain posi...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nThe equation $x^2-kx-12=0$ has only integer...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nThe equation $x^2-kx-12=0$ has only integer...	true	0.102539
Write Python code to solve the task: ATM machines allow 4 or 6 digit PIN codes and PIN codes cannot contain anything but exactly 4 digits or exactly 6 digits. If the function is passed a valid PIN string, return `true`, else return `false`. ## Examples ``` "1234" --> true "12345" --> false "a234" --> fa...	[ { "content": "Write Python code to solve the task:\nATM machines allow 4 or 6 digit PIN codes and PIN codes cannot contain anything but exactly 4 digits or exactly 6 digits. \n\nIf the function is passed a valid PIN string, return `true`, else return `false`.\n\n## Examples \n```\n\"1234\" --> true\n\"12...	[ { "content": "Write Python code to solve the task:\nATM machines allow 4 or 6 digit PIN codes and PIN codes cannot contain anything but exactly 4 digits or exactly 6 digits. \n\nIf the function is passed a valid PIN string, return `true`, else return `false`.\n\n## Examples \n```\n\"1234\" --> true\n\"12...	false	0.021973
Solve the following math problem step-by-step. Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}. A circle has an area of $\pi$ square units. What is the length of the circle's diameter, in units?	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA circle has an area of $\\pi$ square units. What is the length of the circle's diameter, in units?", "role": "user" }, { "content": "Step 1: W...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nA circle has an area of $\\pi$ square units. What is the length of the circle's diameter, in units?", "role": "user" }, { "content": "Step 1: Fi...	true	0.882813
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. The graph of a certain quadratic $y = ax^2 + bx + c$ is a parabola wit...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nThe graph of a certain quadratic $y = ax^2 ...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nThe graph of a certain quadratic $y = ax^2 ...	false	0.057373
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. Solve for $x$, where $x>0$ and $5x^2+9x-18=0$. Express your answer as ...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nSolve for $x$, where $x>0$ and $5x^2+9x-18=...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nSolve for $x$, where $x>0$ and $5x^2+9x-18=...	false	0.01001
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. if there is one larger cube with surface area 600 and no . of smaller ...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nif there is one larger cube with surface ar...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nif there is one larger cube with surface ar...	true	0.933594
Solve the following problem step-by-step: Given the context and corresponding question, choose the correct answer from the options. Context: Scientists typically do their most creative work before the age of forty. It is commonly thought that this happens because <b> aging by itself brings about a loss of creative ca...	[ { "content": "Solve the following problem step-by-step:\nGiven the context and corresponding question, choose the correct answer from the options.\n\nContext: \nScientists typically do their most creative work before the age of forty. It is commonly thought that this happens because <b> aging by itself brings a...	[ { "content": "Solve the following problem step-by-step:\nGiven the context and corresponding question, choose the correct answer from the options.\n\nContext: \nScientists typically do their most creative work before the age of forty. It is commonly thought that this happens because <b> aging by itself brings a...	true	0.267578
Solve the following problem step-by-step: Given the context and corresponding question, choose the correct answer from the options. Context: The economy of Colonia has been in recession for the past eight years. Most companies that have not been forced into bankruptcy have survived thanks to the high efficiency of th...	[ { "content": "Solve the following problem step-by-step:\nGiven the context and corresponding question, choose the correct answer from the options.\n\nContext: \nThe economy of Colonia has been in recession for the past eight years. Most companies that have not been forced into bankruptcy have survived thanks to...	[ { "content": "Solve the following problem step-by-step:\nGiven the context and corresponding question, choose the correct answer from the options.\n\nContext: \nThe economy of Colonia has been in recession for the past eight years. Most companies that have not been forced into bankruptcy have survived thanks to...	true	0.96875
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. what is the ratio whose term differ by 40 and the measure of which is ...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nwhat is the ratio whose term differ by 40 a...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nwhat is the ratio whose term differ by 40 a...	false	0.136719
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. Given the following table: Table title: Technical assistance wait time...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nGiven the following table:\nTable title: Te...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nGiven the following table:\nTable title: Te...	false	0.014954
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. a man buys 25 lts of liquid which contains 20 % of the liquid and the ...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\na man buys 25 lts of liquid which contains ...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\na man buys 25 lts of liquid which contains ...	true	0.75
Write Python code to solve the task: Chef has a binary string S of size N. Chef can perform the following operation on the string: Select any substring of size 3 and reverse it. Find the minimum distance between any two 1s Chef can achieve, by applying the above operation any (possibly zero) number of times. Note: ...	[ { "content": "Write Python code to solve the task:\nChef has a binary string S of size N. Chef can perform the following operation on the string:\nSelect any substring of size 3 and reverse it.\n\nFind the minimum distance between any two 1s Chef can achieve, by applying the above operation any (possibly zero...	[ { "content": "Write Python code to solve the task:\nChef has a binary string S of size N. Chef can perform the following operation on the string:\nSelect any substring of size 3 and reverse it.\n\nFind the minimum distance between any two 1s Chef can achieve, by applying the above operation any (possibly zero...	true	0.125977
Write Python code to solve the task: Illumination Illuminations are displayed in the corridors every year at the JOI High School Cultural Festival. The illuminations consist of N light bulbs, which are lined up in a row from the west side to the east side of the corridor. Each light bulb is either on or off. A machin...	[ { "content": "Write Python code to solve the task:\nIllumination\n\nIlluminations are displayed in the corridors every year at the JOI High School Cultural Festival. The illuminations consist of N light bulbs, which are lined up in a row from the west side to the east side of the corridor. Each light bulb is ei...	[ { "content": "Write Python code to solve the task:\nIllumination\n\nIlluminations are displayed in the corridors every year at the JOI High School Cultural Festival. The illuminations consist of N light bulbs, which are lined up in a row from the west side to the east side of the corridor. Each light bulb is ei...	false	0.34375
Solve the following math problem step-by-step. Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}. For a real number $x,$ find the maximum value of \[\frac{x^4}{x^8 + 2x^6 - 4x^4 + 8x^2 + 16}.\]	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFor a real number $x,$ find the maximum value of\n\\[\\frac{x^4}{x^8 + 2x^6 - 4x^4 + 8x^2 + 16}.\\]", "role": "user" }, { "content": "Step 1: T...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\nFor a real number $x,$ find the maximum value of\n\\[\\frac{x^4}{x^8 + 2x^6 - 4x^4 + 8x^2 + 16}.\\]", "role": "user" }, { "content": "Step 1: Th...	false	0.363281
Solve the following math problem step-by-step. Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}. each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discreti...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\neach month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary ...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\neach month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary ...	true	0.980469
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. If $y=\frac{12x^4+4x^3+9x^2+5x+3}{3x^4+2x^3+8x^2+3x+1}$, at what value...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nIf $y=\\frac{12x^4+4x^3+9x^2+5x+3}{3x^4+2x^...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nIf $y=\\frac{12x^4+4x^3+9x^2+5x+3}{3x^4+2x^...	false	0.160156
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. q - 1 ) of the 84 parents who attended a meeting at a school , 25 volu...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nq - 1 ) of the 84 parents who attended a me...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nq - 1 ) of the 84 parents who attended a me...	true	0.898438
Write Python code to solve the task: Given are a prime number p and a sequence of p integers a_0, \ldots, a_{p-1} consisting of zeros and ones. Find a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \ldots + b_0, satisfying the following conditions: * For each i (0 \leq i \leq p-1), b_i i...	[ { "content": "Write Python code to solve the task:\nGiven are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\n\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n\n* For each...	[ { "content": "Write Python code to solve the task:\nGiven are a prime number p and a sequence of p integers a_0, \\ldots, a_{p-1} consisting of zeros and ones.\n\nFind a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \\ldots + b_0, satisfying the following conditions:\n\n* For each...	true	0.832031
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. James spends 3 hours vacuuming and x times as long on the rest of his ...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nJames spends 3 hours vacuuming and x times ...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nJames spends 3 hours vacuuming and x times ...	true	0.014038
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. What is the smallest four-digit palindrome that is divisible by 4? (A...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nWhat is the smallest four-digit palindrome ...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nWhat is the smallest four-digit palindrome ...	false	0.339844
Solve the following math problem step-by-step. Simplify your answer as much as possible. Present your final answer as \boxed{Your Answer}. 2 distinct vertices of an octagon are chosen at random. What is the probability that they are adjacent?	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n2 distinct vertices of an octagon are chosen at random. What is the probability that they are adjacent?", "role": "user" }, { "content": "Step ...	[ { "content": "Solve the following math problem step-by-step.\nSimplify your answer as much as possible. Present your final answer as \\boxed{Your Answer}.\n2 distinct vertices of an octagon are chosen at random. What is the probability that they are adjacent?", "role": "user" }, { "content": "Step ...	true	0.96875
Write Python code to solve the task: The Ohgas are a prestigious family based on Hachioji. The head of the family, Mr. Nemochi Ohga, a famous wealthy man, wishes to increase his fortune by depositing his money to an operation company. You are asked to help Mr. Ohga maximize his profit by operating the given money durin...	[ { "content": "Write Python code to solve the task:\nThe Ohgas are a prestigious family based on Hachioji. The head of the family, Mr. Nemochi Ohga, a famous wealthy man, wishes to increase his fortune by depositing his money to an operation company. You are asked to help Mr. Ohga maximize his profit by operatin...	[ { "content": "Write Python code to solve the task:\nThe Ohgas are a prestigious family based on Hachioji. The head of the family, Mr. Nemochi Ohga, a famous wealthy man, wishes to increase his fortune by depositing his money to an operation company. You are asked to help Mr. Ohga maximize his profit by operatin...	true	0.996094
Tool available: [1] Python interpreter When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. Solve the following math problem step-by-step. Simplify your answer as much as possible. what is the least positive integer x for which ( x ^ 2 ) + 164 is divi...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nwhat is the least positive integer x for wh...	[ { "content": "Tool available:\n[1] Python interpreter\nWhen you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment.\nSolve the following math problem step-by-step.\nSimplify your answer as much as possible.\nwhat is the least positive integer x for wh...	false	0.211914
Write Python code to solve the task: You are given a pair of integers $(a, b)$ and an integer $x$. You can change the pair in two different ways: set (assign) $a := \|a - b\|$; set (assign) $b := \|a - b\|$, where $\|a - b\|$ is the absolute difference between $a$ and $b$. The pair $(a, b)$ is called $x$-magic if $x$ is...	[ { "content": "Write Python code to solve the task:\nYou are given a pair of integers $(a, b)$ and an integer $x$.\n\nYou can change the pair in two different ways:\n\nset (assign) $a := \|a - b\|$;\n\nset (assign) $b := \|a - b\|$,\n\nwhere $\|a - b\|$ is the absolute difference between $a$ and $b$.\n\nThe pair $(a, ...	[ { "content": "Write Python code to solve the task:\nYou are given a pair of integers $(a, b)$ and an integer $x$.\n\nYou can change the pair in two different ways:\n\nset (assign) $a := \|a - b\|$;\n\nset (assign) $b := \|a - b\|$,\n\nwhere $\|a - b\|$ is the absolute difference between $a$ and $b$.\n\nThe pair $(a, ...	true	0.016357