prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.428e-4 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 37.9 g/mol |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $633.6 |
[
{
"content": "Let $F$ be a field of characteristic $p > 0$ and let $f(t) = t^p - t - a \\in F[t]$. Suppose also that $a \\neq b^p - b$ for any $b \\in F$. Determine the Galois group $Gal(K/F)$, where $K$ is a splitting field of $f$. \\( \\text{Provide your answer in terms of group structure.} \\)",
"role": ... | \mathbb{Z}/p\mathbb{Z} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.53i-2.71j |
[
{
"content": "Given a real-valued function $f(x, y)$ defined on an open set $U$ in $\\mathbb{R}^2$, where $f$ is smooth in $x$ for each fixed $y$ and its partial derivatives with respect to $x$ are absolutely continuous in $y$ for each fixed $x$. Furthermore, $\\frac{\\partial}{\\partial_y} f$ exists everywhere... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $5,200 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.77 days |
[
{
"content": "Find the six-digit natural number $N$ with a digit sum of $43$, where exactly one of the following statements is false: (1) $N$ is a perfect square, (2) $N$ is a perfect cube, and (3) $N < 500000$. Determine the value of $N$. Given: The smallest six-digit number with a digit sum of $43$ is $169999... | 499849 |
[
{
"content": "Let $R$ be a commutative ring with $1$. Suppose that $I$ is an ideal of $R$ which is maximal with respect to the property that it is proper and not prime. Prove that $I$ is contained in at most two other proper ideals of $R$. ",
"role": "user"
}
] | 2 |
[
{
"content": "Given a sample $X$ of one hundred observations $X_i$ such that $\\forall i: X_i \\in \\mathbb{N}[-101, 101]$, with unique minimum $A$ and unique maximum $B$, the mean of the sample is $M = \\bar{X}$. After negating $A$ and $B$, the mean of the modified sample becomes $-M$. What is the maximum poss... | 1 |
[
{
"content": "Determine whether there exist 2000 distinct unit fractions whose sum is equal to 1.",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\( g(v(x)) = \\int_{-1}^{1} (x^2-1) v(x) \\, dx \\) be a linear functional defined for all \\( v \\in (C[-1,1], ||.||_\\infty) \\). Find the norm \\( ||g|| \\).",
"role": "user"
}
] | \dfrac{4}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 43.7 mF |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 42.4 atm |
[
{
"content": "Determine the number of different subgroups of order 9 that are isomorphic to $C_3 \\times C_3$ in the symmetric group $S_6$. Provide your answer as a single integer.",
"role": "user"
}
] | 10 |
[
{
"content": "Given that the polynomial \\( f(x) = x^3 - 3x + 2 \\) has roots \\( a, b, c \\), find the value of \\( ((a-b)(b-c)(c-a))^2 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to \\infty} \\left[\\left(\\left(\\frac{x+1}{x-1}\\right)^x - e^2\\right)x^2\\right] \\] by substituting \\( x \\to \\frac{1}{t} \\) and considering \\[ L = \\lim_{t \\to 0} \\frac{\\left(\\frac{1+t}{1-t}\\right)^{1/t} - e^2}{t^2} \\]",
"role": "user"
}
] | \dfrac{2}{3}e^2 |
[
{
"content": "Evaluate the contour integral \\( \\int_C ze^{3/z}\\,dz \\), where \\( C \\) is the contour given by \\( |z|=2 \\), oriented in a counter-clockwise direction.",
"role": "user"
}
] | 9\pi i |
[
{
"content": "Evaluate the limit: $$\\lim\\limits_{n \\to \\infty} \\frac{\\sqrt{1} + \\sqrt{2} + \\dots + \\sqrt{n}}{n\\sqrt{n}}.$$",
"role": "user"
}
] | \dfrac{2}{3} |
[
{
"content": "Luna writes down all the five-digit numbers that contain each of the digits 1, 2, 3, 4 and 5 exactly once. What is the smallest number in Luna's list that is divisible by 6?",
"role": "user"
}
] | 12354 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -$503.06 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4C_3H_5(NO_3)_3 -> 12CO_2 + 10H_2O + 6N_2 + O_2 |
[
{
"content": "Identify the 5 elements in the icosahedral group of order 60 that have a stabilizer of order 12.",
"role": "user"
}
] | 5 |
[
{
"content": "Find the order of the quotient group \\( \\mathbb{Z}^3 / \\langle (2,1,5), (1,2,10), (2,1,7) \\rangle \\). Use a method other than the presentation matrix approach.",
"role": "user"
}
] | 6 |
[
{
"content": "Find the value of \\( \\lfloor (\\sqrt{21}+\\sqrt{29})^{1984}\\rfloor \\mod 100 \\).",
"role": "user"
}
] | 71 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -298.0 cm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The criteria to be met for offsetting a note payable with an account receivable are that the amounts can be reliably determined, the reporting party intends to set off, right of set off must be with party whose payment is earlier if due dates differ, and enforceability should be there according to law. |
[
{
"content": "Determine the radius of convergence of the Taylor series for \\( \\frac{\\sin x}{1+x^2} \\) centered at \\( x=0 \\).",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1. Investment in McKenzie: Debit $600,000
Cash: Credit $600,000
2. Investment in McKenzie: Debit $2,000
Retained Earnings - prior period adjustment (2014 equity income): Credit $2,000
3. Investment in McKenzie: Debit $115,667
Equity Income - Investment in McKenzie: Credit $115,667
4. Cash: Debit $44,000
Investment in M... |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 130071.58 |
[
{
"content": "Find a solution $u(x,y)$ of Laplace’s equation on the domain $-\\infty < x < \\infty$ and $0 < y < \\infty$ such that $u(x,0) = x^{1/2}$ for $0 < x < \\infty$. Determine $u(x,0)$ for $-\\infty < x < 0$. Use conformal mapping techniques to solve the problem.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the function \\( P(x) \\), where \\( P(x) \\) is a polynomial of degree 101, can be a bijective function from \\( \\mathbb{R} \\) to \\( \\mathbb{R} \\). Answer \"True\" if it can be bijective, or \"False\" if it cannot.",
"role": "user"
}
] | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.3e-2 year |
[
{
"content": "Determine the number of critical points where the function \\( f(x) = \\begin{cases} x^2 e^{-x^2-x^{-2}} & \\text{if } x \\neq 0, \\\\ 0 & \\text{if } x = 0 \\end{cases} \\) has a local extremum.",
"role": "user"
}
] | 3 |
[
{
"content": "Determine the modulus of continuity of the function \\( f(x) = \\sin\\left(\\frac{1}{x}\\right) \\) on the interval \\( I = (0, 1) \\). The modulus of continuity is defined as \\( w(f,r) = \\sup\\{|f(x)-f(y)| : x,y \\in I, |x-y| \\leq r\\} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Determine all values of the parameter \\( a \\) for which the system of equations \\( \\left\\{\\begin{array}{l} |y+x+8|+|y-x+8|=16 \\\\ (|x|-15)^{2}+(|y|-8)^{2}=a \\end{array}\\right. \\) has exactly two solutions.",
"role": "user"
}
] | 49 |
[
{
"content": "In a 100x100 grid, each unit square contains a natural number. A rectangle with sides parallel to the grid is called \"good\" if the sum of the numbers inside the rectangle is divisible by 17. We can paint all unit squares in a \"good\" rectangle, and no unit square can be painted more than once. ... | 9744 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.79 g/L |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 122.22 |
[
{
"content": "Calculate the expected value of the area of the rectangle EFDG formed inside a unit square ABCD, where point E is randomly and uniformly chosen within the interior of the square.",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.25 m^3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $16,211.85 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 144.68 N |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.8 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.76m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1320 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $4.43 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 317 mi/h |
[
{
"content": "Find the natural number \\( n \\) that satisfies the equation:\n\\[ \\dfrac{1}{2}C_{2n}^1 - \\dfrac{2}{3} C_{2n}^2 + \\dfrac{3}{4} C_{2n}^3 - \\dfrac{4}{5} C_{2n}^4 + \\cdots - \\dfrac{2n}{2n+1} C_{2n}^{2n} =\\dfrac{1}{2013}. \\]",
"role": "user"
}
] | 1006 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 12.2 cm |
[
{
"content": "Two ships are moving as follows: Ship A is 1 mile due north of a pier and is traveling N $30^o$ E at 3 mph. Ship B is $\\frac{3}{4}$ mile east of the pier and is traveling east at 7 mph. Determine the rate at which the angle between the two ships' paths is changing.",
"role": "user"
}
] | -\dfrac{3}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 86.4 g |
[
{
"content": "Let $p(x)$ be the polynomial of degree at most 8 such that\n\\[p(n) = \\frac{1}{n}\\]for $n = 1,$ 2, 3, $\\dots,$ 9. Find $p(10).$",
"role": "user"
}
] | \frac{1}{5} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.414e-22 J |
[
{
"content": "In the acute triangle $ABC$, let $H$ be the orthocenter and $O$ the circumcenter. The altitude from $A$ meets $BC$ at $P$. Given that the distance from $O$ to line $AC$ is $2$ and $PH = 1$, calculate the power of point $P$ with respect to the circumcircle of triangle $ABC$.",
"role": "user"
... | -5 |
[
{
"content": "Determine whether the integral of a nonconstant monomial over the unit disk vanishes. Specifically, evaluate the following integral and determine if it equals zero for all positive integers \\( n \\):\n\\[\n\\int_{-1}^{1} \\int_{-1}^{1} [a^2+b^2 < 1] (a+bi)^n \\;\\text{d}a\\text{d}b = 0 \\;\\; \\t... | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $39,600 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.67 mm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | r_{2,x} = -39.78 m, r_{2,y} = 41.42 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 12.35% |
[
{
"content": "Simplify $(2x - 5)(x + 7) - (x + 5)(2x - 1)$.",
"role": "user"
}
] | -30 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | m^3/As |
[
{
"content": "Find a number \\( x \\) such that for all integers \\( a \\) in the set \\( \\{0, 1, 2, \\ldots, 1926\\} \\), the congruence \\( a^x \\equiv a \\pmod{1926} \\) holds. Exclude \\( x = 1 \\) from consideration.",
"role": "user"
}
] | 319 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.88% |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 0^+} x^{(x^x-1)}. \\]",
"role": "user"
}
] | 1 |
[
{
"content": "Use Stokes' Theorem to evaluate the integral \\( \\iint_\\Sigma y \\, \\mathrm{d}y \\, \\mathrm{d}z + z \\, \\mathrm{d}z \\, \\mathrm{d}x + x \\, \\mathrm{d}x \\, \\mathrm{d}y \\), where \\( \\Sigma \\) is the upper half-sphere oriented outwardly. The hint provided is that \\( (y,z,x) = \\text{Cur... | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 45.8333 m^2 |
[
{
"content": "In a 3D cubic grid of size $8 \\times 8 \\times 8$, how many straight lines can be formed that contain exactly 8 symbols in a row?",
"role": "user"
}
] | 244 |
[
{
"content": "Find the unit digit of the expression \\((5+\\sqrt{24})^{1234}+(5-\\sqrt{24})^{1234}\\).",
"role": "user"
}
] | 8 |
[
{
"content": "Find the smallest positive integer \\( n \\) such that the equation \\[ x_{1}^{3} + x_{2}^{3} + \\cdots + x_{n}^{3} = 2002^{2002} \\] has integer solutions \\((x_{1}, x_{2}, \\ldots, x_{n})\\).",
"role": "user"
}
] | 4 |
[
{
"content": "Determine the dimension of the range space of the linear operator $T$ defined on the real vector space $C[0, 1]$, where $T$ is given by $$(Tf)(x) =\\int_{0}^{1}\\sin(x + y)f(y) dy,\\quad x\\in[0, 1].$$",
"role": "user"
}
] | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 164008 |
[
{
"content": "How many squares have all four vertices on the 5 by 5 rectangular grid of dots below? Two such squares are displayed. [asy]\nsize(50);\nfor(int i = 0; i < 5; ++i){\n\nfor(int j = 0; j < 5; ++j){\n\ndot((i,j));\n\n}\n}\ndraw((0,4)--(1,4)--(1,3)--(0,3)--cycle,linewidth(0.7));\ndraw((2,0)--(4,1)--(3,... | 50 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 43 N |
[
{
"content": "If $u,v \\in \\mathbb{R}^n$ and $u^TAv = u^Tv$ for a square matrix $A$ of order $n$, does it necessarily imply that $A = I_n$? Answer yes or no and justify your answer.",
"role": "user"
}
] | No |
[
{
"content": "Calculate the total curvature of the logarithmic spiral given by the parameterization \\( \\exp(t) \\cdot (\\cos(t), \\sin(t)) \\) for \\( t \\in [0, 2\\pi] \\).",
"role": "user"
}
] | 2\pi |
[
{
"content": "Find all eigenvalues and eigenvectors of the linear operator $T: P(\\mathbb{R}) \\rightarrow P(\\mathbb{R})$ defined by $T(p) = p'$, where $P(\\mathbb{R})$ is the space of polynomials with real coefficients.",
"role": "user"
}
] | 0 |
[
{
"content": "Let $V$ be the vector space of polynomials of degree less than or equal to $3$ and let \\( \\langle p, q \\rangle = p(0)q(0) + p'(0)q'(0) + p(1)q(1) + p'(1)q'(1) \\) be an inner product on $V$. Find the angle between the polynomials \\( p_1(x) = 2x^3 - 3x^2 \\) and \\( p_2(x) = 1 \\).",
"role"... | \dfrac{3\pi}{4} |
[
{
"content": "Determine the radius of convergence for the series represented by the ordinary generating function $f(x) = \\tan x$.",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Consider the curves defined by the functions \\(y=mx\\) and \\(y=\\frac{x}{x^2+1}\\), where \\(0<m<1\\). The area \\(A\\) of the region enclosed by these curves is given by the integral \\(A=2\\int_{a}^{0}(mx-\\frac{x}{x^2+1})dx\\). Show that this area can be expressed as \\(A=m-\\ln|m-1|\\).",
... | A = m - \ln|m - 1| |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 649.52 m/s |
[
{
"content": "Evaluate the limit: $$\\lim_{t \\to 1} \\left( \\tan \\left( \\frac{\\pi t}{4} \\right) \\right)^{\\frac{2t}{1-t^2}}$$",
"role": "user"
}
] | e^{-\pi/2} |
[
{
"content": "Consider a carnival game that starts with two dollars in a bowl. Each turn, a coin is flipped. If the result is heads, the carnival doubles the money in the bowl. If the result is tails, you take the money out of the bowl. What is the expected value of the money you would receive from this game?",... | \infty |
[
{
"content": "On an infinite line AB, construct a point C such that the rays CM and CN, connecting C with two given points M and N on the same side of AB, form congruent angles with the rays CA and CB, respectively. Describe the steps to construct this point C using a compass and ruler.",
"role": "user"
}... | C |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.6 degree Celsius |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.806104674 seconds |
[
{
"content": "Determine the number of non-invertible elements in the multiplicative group $(\\mathbb{Z}/p^n\\Bbb{Z})^\\times$, where $p$ is a prime number.",
"role": "user"
}
] | p^{n-1} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 98/n N |
[
{
"content": "Find the minimum value of the length of a segment of a tangent to the ellipse \\(\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1\\) intercepted by the coordinate axes. The length of the segment is given by \\(\\sqrt{a^2\\sec^2\\theta+b^2\\csc^2\\theta}\\).",
"role": "user"
}
] | a + b |
[
{
"content": "Determine whether the following statement is true or false: For any integer $m > 1$, among any $2m$ consecutive positive integers, there are at least two numbers that cannot be divided by odd prime numbers greater than or equal to $2m$. Provide a justification for your answer.",
"role": "user"... | False |
[
{
"content": "In \\(\\triangle ABC\\), which is an equilateral triangle, point \\(O\\) is located inside the triangle such that \\(\\angle OAB = x\\), \\(\\angle OBC = 42^\\circ\\), and \\(\\angle OCB = 54^\\circ\\). Find the value of \\(x\\) without using trigonometry.",
"role": "user"
}
] | 48 |
[
{
"content": "Chuck the llama is tied to the corner of a $2\\text{ m}$ by $3\\text{ m}$ shed on a $3\\text{ m}$ leash. How much area (in square meters) does Chuck have in which to play if he can go only around the outside of the shed? [asy]\ndraw((0,0)--(15,0)--(15,10)--(0,10)--cycle,black+linewidth(1));\ndraw(... | 7\pi |
[
{
"content": "Find all real numbers $k$ that minimize the maximum value of $f(x) = |x^2 - x - k|$ over the interval $0 \\le x \\le 1$.",
"role": "user"
}
] | -\dfrac{1}{8} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 56670 J |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 60.1% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 19079.28 |
[
{
"content": "Evaluate the improper integral: $$\\int_{0}^{\\infty} \\frac{\\sin x}{x^{3/2}} \\, dx.$$",
"role": "user"
}
] | \sqrt{2\pi} |
[
{
"content": "Evaluate the integral \\( I = \\int_{0}^{\\pi} \\frac{\\sin(x)\\ln(x)}{\\ln(\\pi x - x^2)} \\, dx \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether the Bernoulli measure of the infinite word \\( x = (\\ldots, y_1, y_1, y_1, \\ldots) \\), which consists entirely of the repeated entry \\( y_1 \\), is zero. Assume the Bernoulli measure \\( \\mu \\) is defined on finite blocks as \\( \\mu([y_1,y_2,\\ldots,y_n]m) = \\prod_{j=1}^n... | 0 |
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