prompt list | ground_truth string |
|---|---|
[
{
"content": "Solve for \\( F \\) in the equation:\n\\[\n\\frac{aF - b}{\\sqrt{(aF - b)^2 + (cF - d)^2 + (eF - g)^2}} = \\frac{hF - i}{\\sqrt{(hF - i)^2 + (jF - k)^2 + (mF - n)^2}}\n\\] where all other variables are known.",
"role": "user"
}
] | F |
[
{
"content": "Compute \\( sd(sd(sd(1976^{1976}))) \\), where \\( sd(n) \\) represents the sum of the digits of \\( n \\).",
"role": "user"
}
] | 7 |
[
{
"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... | 0.016M |
[
{
"content": "Find the limit: $$\\lim\\limits_{n\\rightarrow\\infty}\\left(\\frac{n^2 + 1}{n^2 - 2}\\right)^{n^2}$$",
"role": "user"
}
] | e^3 |
[
{
"content": "Is it possible to introduce a new metric on any metric space such that the new metric is bounded by 1 and preserves the topology of the original metric space?",
"role": "user"
}
] | 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... | 1612 m/s |
[
{
"content": "If a finite group $G$ is solvable, is the derived subgroup $[G,G]$ nilpotent?",
"role": "user"
}
] | No |
[
{
"content": "Evaluate the limit using polar coordinates: $$\\lim_{(x,y)\\to(0,0)} {\\frac{x^4y^3}{x^6+y^8}}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate $\\lfloor-2.54\\rfloor+\\lceil25.4\\rceil$.",
"role": "user"
}
] | 23 |
[
{
"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... | [Ar]4s^23d^104p^1 |
[
{
"content": "Evaluate the integral \\( \\int_{|z-i| = 10} \\left(z+\\frac{1}{z}\\right)^4 \\, dz \\) using the Residue Theorem.",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the work done by the force \\( \\vec{F}=(x-y) \\vec{i}+\\vec{j} \\) when moving along the semicircular path \\( x^{2}+y^{2}=4 \\) (with \\( y \\geq 0 \\)) from point \\( M(2,0) \\) to point \\( N(-2,0) \\).",
"role": "user"
}
] | 2\pi |
[
{
"content": "Verify Gauss' Theorem for the vector field \\( F = (x^2, -y, z) \\) over the region \\( V \\), where \\( V \\) is the solid cylinder defined by \\( y^2 + z^2 \\le 9 \\) and \\( 0 \\le x \\le 2 \\).",
"role": "user"
}
] | 36\pi |
[
{
"content": "Let $X$ be a matrix defined as $X = [x_{ij}]$, where $x_{ij}=c_id_j$ for $1 \\leq i\\leq n$ and $1 \\leq j\\leq n$, and $c_i, d_j \\in \\mathbb{R}$. If $X^4=81X$, find the trace of $X$, denoted as $\\operatorname{Tr}(X)$. \\( \\operatorname{Tr}(X) = \\boxed{?} \\)",
"role": "user"
}
] | 3\sqrt[3]{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... | 6.11% |
[
{
"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... | 1.07m |
[
{
"content": "Evaluate the limit: \\(\\lim_{x\\to +\\infty}\\frac {\\zeta(1+\\frac 1x)}{\\Gamma(x)}\\)",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of distinct terms in the expansion of \\( \\left(x + \\frac{1}{x} + x^2 + \\frac{1}{x^2} \\right)^{20} \\).",
"role": "user"
}
] | 81 |
[
{
"content": "Fifty viewers came to the cinema, and their total age is 1555 years, with no two viewers having the same age. Determine the maximum value of \\( k \\) such that you can select 16 viewers whose total age is at least \\( k \\) years.",
"role": "user"
}
] | 790 |
[
{
"content": "The values of $a$, $b$, $c$ and $d$ are 1, 2, 3 and 4, but not necessarily in that order. What is the largest possible value of the sum of the four products $ab$, $bc$, $cd$ and $da$?",
"role": "user"
}
] | 25 |
[
{
"content": "Determine the number of roots of the equation \\( z^4 - 5z + 1 = 0 \\) that lie within the annulus defined by \\( 1 \\leq |z| \\leq 2 \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Evaluate the limit: \\[ A = \\lim_{x\\to\\infty}\\left(\\frac{x^2-3x+1}{x^2+x+2}\\right)^{2x-5} \\]",
"role": "user"
}
] | e^{-8} |
[
{
"content": "Determine whether there exists a differentiable convex function, other than a constant function, that has multiple global minima. Answer with 'Yes' or 'No'.",
"role": "user"
}
] | Yes |
[
{
"content": "In a measure space $(X, \\mathcal F, \\mu)$ with $\\mu(X)=1$, there are $n$ measurable sets $F_1, F_2, \\ldots, F_n$ such that $\\mu(F_j) \\geq 1/2$ for all $j$. Determine the smallest integer $k$ such that there exists a subset of indices $\\{i_1, i_2, \\ldots, i_k\\}$ for which $F_{i_1} \\cap F_... | \lceil n/2 \rceil |
[
{
"content": "Solve the equation: \\(2^{2x} + 2^{2x - 1} = 3^{x + 0.5} + 3^{x - 0.5}\\).",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "Consider the ring of formal power series $R[[x]]$. Define a metric on $R[[x]]$ for two series $\\sum a_{n}x^{n}$ and $\\sum b_{n}x^{n}$ as $d((a_n),(b_n))=2^{-k}$, where $k$ is the smallest natural number such that $a_{k} \\neq b_{k}$, or zero if no such $k$ exists. Let $\\{x_{i}: i \\in \\mathbb{... | 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... | 2.54 m/s |
[
{
"content": "Determine whether the following statement is true or false: For any positive definite matrix $A$, the trace of $A^{-1}$ is equal to the sum of the reciprocals of the eigenvalues of $A$. Provide a justification for your answer.",
"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... | $38,183.86 |
[
{
"content": "Approximate the integral \\( \\int_3^4 \\frac{x}{\\sqrt{(7x-10-x^2)^3}} \\, dx \\) and determine which of the following intervals contains its value:\n\n(a) \\( \\left(\\frac{9}{10}, \\frac{19}{20}\\right) \\)\n(b) \\( \\left(\\frac{19}{20}, 1\\right) \\)\n(c) \\( \\left(1, \\frac{21}{20}\\right) ... | D |
[
{
"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... | $335,000 |
[
{
"content": "Find all functions \\( g: \\mathbb{R}^+ \\to \\mathbb{R} \\) that satisfy the differential equation \\( g'(x) = g(\\sqrt{x}) \\) and the condition \\( \\lim\\limits_{x \\to 0} g(x) = 0 \\).",
"role": "user"
}
] | 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... | 2SO_3^(2-) + 2Be -> Be_2O_3^(2-) + S_2O_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... | The rate of acceleration is approximately 6.02 units/s^2, and the direction is approximately -85.2 degrees. |
[
{
"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... | 0.36 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... | $63,917.37 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to+\\infty} \\frac{1}{n\\log(n)}\\sum_{k=4}^{n}\\frac{2k}{k^2-2k-3} \\] Find the value of \\( \\alpha \\) such that \\( \\lim_{n\\to+\\infty} \\frac{1}{n\\log(n)}\\sum_{k=4}^{n}\\frac{2k}{k^2-2k-3} = \\alpha \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the values of $p$ for which the integral \\( \\int_1^{\\infty} \\frac{\\sin^2 x}{x^p} \\, dx \\) converges.",
"role": "user"
}
] | p > 1 |
[
{
"content": "Given the parametric equations of a curve at any point \\(\\theta\\): \\[x = a\\cos(\\theta) + a\\theta\\sin(\\theta)\\] \\[y = a\\sin(\\theta) - a\\theta\\cos(\\theta)\\] find the distance from the origin to the normal of this curve at any \\(\\theta\\).",
"role": "user"
}
] | a |
[
{
"content": "Determine whether for a prime number \\( p \\equiv 1 \\pmod{4} \\), there exists an element in the finite field \\( \\mathbb{F}_p \\) such that its square is \\(-1\\).",
"role": "user"
}
] | 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... | $3 |
[
{
"content": "Let \\( F(x) \\) be a polynomial of degree 2013 with integer coefficients such that \\( F(0) = 1 \\) and \\( F(3) \\) is a divisor of 2013. Determine the largest possible value of \\( F(3) \\).",
"role": "user"
}
] | 61 |
[
{
"content": "Consider all quadrilaterals $ABCD$ such that $AB=14$, $BC=9$, $CD=7$, and $DA=12$. What is the radius of the largest possible circle that fits inside or on the boundary of such a quadrilateral?\n$\\textbf{(A)}\\ \\sqrt{15} \\qquad \\textbf{(B)}\\ \\sqrt{21} \\qquad \\textbf{(C)}\\ 2\\sqrt{6} \\qqu... | 2\sqrt{6} |
[
{
"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... | $11,497.89 |
[
{
"content": "Show that \\( R(x) = o(x^3) \\) given that \\[ R(x) = 4! \\, x^4 \\int _0^{\\infty} \\frac{1}{(1+xt)^{5}}e^{-t} \\, \\, dt. \\]",
"role": "user"
}
] | R(x) = o(x^3) |
[
{
"content": "Given that X is a continuous random variable with density function \\( f(x) = \\frac{2}{x^2} \\) for \\( x \\geq 2 \\) and 0 otherwise, find the density function of \\( Y = \\frac{X}{X-1} \\) for \\( 1 < y \\leq 2 \\).",
"role": "user"
}
] | \dfrac{2}{y^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... | Date: April 1, 2010
Account Description: Financial Asset - Fair value through other comprehensive income | Debit: 166,300
Account Description: Interest Receivable | Debit: 2,400
Account Description: Cash | Credit: 168,700 |
[
{
"content": "Determine the limiting distribution of the sequence of random variables $Y_n = \\frac{X_n - n}{n^2}$, where $X_n$ is uniformly distributed over the interval $[n, n^2]$ for $n = 1, 2, 3, \\dots$. What does $Y_n$ converge to in distribution as $n \\to \\infty$?",
"role": "user"
}
] | U(0,1) |
[
{
"content": "Adi the Baller is shooting hoops and makes a shot with probability $p$. He continues shooting until he misses. The value of $p$ that maximizes the probability of making between 35 and 69 (inclusive) buckets can be expressed as $\\frac{1}{\\sqrt[b]{a}}$, where $a$ is a prime number and $b$ is a pos... | 37 |
[
{
"content": "Calculate the limit: \\[ \\lim_{n\\to\\infty} \\left(1 + \\frac{1}{n}\\right) \\, e^{\\frac{1}{n} \\, \\ln\\left(1 + \\frac{1}{n}\\right)} \\, e^{\\ln n/n} \\] as \\( n \\) approaches infinity.",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the radical of the ideal \\((4,x)\\) in the ring \\(\\mathbb{Z}[x]\\). Verify if the following calculation is correct:\n\\[\nr(4,x) = r(4) \\cap r(x) = r(2^2) \\cap r(x) = r(2) \\cap r(x) = r(2,x) = (2,x).\n\\]",
"role": "user"
}
] | (2, x) |
[
{
"content": "Let $\\mathcal{H}^{\\oplus n}$ denote the n-dimensional Hilbert space. Define a linear operator $A = [a_{i,j}]: \\mathcal{H}^{\\oplus n} \\to \\mathcal{H}^{\\oplus n}$ by\n\\[\nA\\begin{bmatrix}\nh_{1}\\\\\n\\vdots\\\\\nh_{n}\n\\end{bmatrix}=\n \\begin{bmatrix}\n\\sum_{k=1}^{n}a_{1k}h_{k}\\\\\n \... | 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... | 11.97 kg cycles^2/ sec^2 |
[
{
"content": "Let \\( AB \\) be the diameter of a semicircle \\( \\Gamma \\). Two circles, \\( \\omega_1 \\) and \\( \\omega_2 \\), externally tangent to each other and internally tangent to \\( \\Gamma \\), are tangent to the line \\( AB \\) at \\( P \\) and \\( Q \\), respectively, and to the semicircular arc... | 40 |
[
{
"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... | 24 cm |
[
{
"content": "Let $p(x, y)$ be a complex polynomial in two variables. Consider the set $G \\subset \\mathbb{C}$, which consists of all $y$ for which every root of the polynomial $p(\\cdot, y)$ is simple. If $G = \\emptyset$, does it imply that $p$ has a square factor? In other words, is $G$ non-empty whenever $... | Yes |
[
{
"content": "Determine the minimum size of a test bank, \\( n \\), such that when 20 people each take a challenge consisting of 9 unique questions drawn from this bank, the probability of having exactly 3 repeated questions is at least 95%.",
"role": "user"
}
] | 177 |
[
{
"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... | Circular arc of radius R = d/(pi-alpha), where d is the length of the flexible strip and alpha is the angle between the two solid objects. |
[
{
"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... | -5.00 nC |
[
{
"content": "In a triangle with angles \\(A, B, C\\) and sides \\(a, b, c\\) opposite to their respective angles, find \\(\\tan C\\) given that:\n\\[ c^2 = \\frac{a^3 + b^3 + c^3}{a + b + c} \\]",
"role": "user"
}
] | \sqrt{3} |
[
{
"content": "Evaluate the limit \\( \\lim_{q\\rightarrow 1^-}\\frac{\\phi^5(q)_{\\infty}}{\\phi(q^5)_{\\infty}} \\), where the Euler function is defined as \\( \\phi(q)=\\prod_{n=1}^{\\infty}(1-q^{n}) \\) and \\( q=\\exp(2\\pi i \\tau) \\) with \\( |q|<1 \\).",
"role": "user"
}
] | 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... | 2.61e7 yr |
[
{
"content": "Given the differential equation \\( y' = \\frac{x - y - 1}{x - y - 2} \\) with the initial condition \\( y(0) = 2 \\), find the value of \\( y(6) \\). Choose the correct option: \\( \\text{a. } -10, \\text{ b. } 0, \\text{ c. } 2, \\text{ d. } 4, \\text{ e. } 6, \\text{ f. } 8 \\).",
"role": "... | E |
[
{
"content": "Calculate the volume between the surfaces defined by the equations \\(x^2 + y^2 = z\\) and \\(2x + 2y + z = 2\\). Determine the correct order of subtraction for the integration to find the volume.",
"role": "user"
}
] | 8\pi |
[
{
"content": "Determine if the sequence $b_r$, defined by the condition $\\gcd(C_n+1, C_n-1) > 1$ where $C_n = \\frac{\\binom{2n}{n}}{n+1}$ is the Catalan sequence, is equal to $2^n - 1$ for $n \\leq 4200$. The starting terms for $b_r$ are: 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095.",
"role": "us... | 2^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... | 72 m/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... | 1 to 1,000 nm |
[
{
"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... | 46.46 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... | 7.860 |
[
{
"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... | 5.24 m |
[
{
"content": "Let $K$ be a field of characteristic zero and $X$ be a projective variety over $\\text{Spec} K$. Denote by $\\bar{K}$ the algebraic closure of $K$. Let $\\bar{X}$ be the fiber product $X \\times_K \\bar{K}$. Suppose that $\\bar{X}$ is a smooth Fano variety. Is $X$ also a Fano variety?",
"role"... | 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... | Secondary pollutants that may form from particulate matter include haze (secondary organic aerosol), acid rain, and smog. |
[
{
"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... | 691 |
[
{
"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... | 100 m/s |
[
{
"content": "Given a bounded open set $V$ in $\\mathbb{R}^{n}$ with $n>1$, determine if it is possible to find an infinite sequence of pairwise disjoint open sets $(C_{n})$ such that each $C_{n}$ is contained in the closure of $V$ and the boundary of $C_{n}$ lies within the boundary of $\\overline{V}$. Answer ... | No |
[
{
"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... | 0.8% |
[
{
"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... | 3.2e-19 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... | 0.6 mol kg^(-1) |
[
{
"content": "Calculate the integral \\( \\int_{-\\infty}^{\\infty} \\frac{x \\sin(\\pi x)}{(x-3)(x-2)} \\, dx \\) using the Residue Theorem.",
"role": "user"
}
] | -5\pi |
[
{
"content": "Determine whether the inverse of a power series \\( p(z) = z + a_2z^2 + a_3z^3 + \\ldots \\), where \\( a_n \\) are integers for \\( n \\geq 2 \\), also has integer coefficients.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$\\lim _{n\\to \\infty }\\left(\\frac{\\left(4n-4-2a_n\\right)}{\\pi }\\right)^n$$ where $$a_n=\\int _1^n\\:\\frac{2x^2}{x^2+1}dx$$.",
"role": "user"
}
] | e^{-\frac{4}{\pi}} |
[
{
"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... | 20.62 s |
[
{
"content": "What is the minimum number of orthogonal matrices required to express the matrix $M_{i,j}$, which is a standard basis matrix of size $n > 1$, as a linear combination of those orthogonal matrices?",
"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... | 7.54 g/cm^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... | 0.4 metric tons |
[
{
"content": "Solve the congruence equation: \\(x^5 \\equiv 3 \\pmod{19}\\).",
"role": "user"
}
] | 10 |
[
{
"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... | 0.54F |
[
{
"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... | 1.15 g |
[
{
"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... | theory |
[
{
"content": "Let $a$ and $b$ be any two real numbers, and let $f$ and $g$ be continuous functions on the interval $[a, b]$. If $\\int_a^b f(x) \\, dx > 0$ and $\\int_a^b g(x) \\, dx < 0$, is it true that $\\int_a^b f(x)g(x) \\, dx < 0$?",
"role": "user"
}
] | No |
[
{
"content": "Determine the number of ways to distribute 10 distinct items into 4 distinct groups such that each group contains an odd number of items.",
"role": "user"
}
] | 130560 |
[
{
"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... | h |
[
{
"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... | 955.1N |
[
{
"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... | -$177.62 |
[
{
"content": "Let $A$ and $B$ be compact metric spaces with Borel probability measures $m_A$ and $m_B$, respectively. Suppose $f: A \\to B$ is a continuous surjection. If $m_A(K) = 1$ for a Borel set $K \\subseteq A$, is it true that $m_B(f(K)) = 1$? Assume $A$ is second-countable.",
"role": "user"
}
] | No |
[
{
"content": "Determine the values of \\( q \\) for which the integral \\( \\int_0^1 x^q \\left( \\frac{1}{x} - \\frac{1}{\\sin(x)} \\right) \\, dx \\) converges.",
"role": "user"
}
] | q > -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... | $11,255 |
[
{
"content": "Given an integer $P$ and an odd positive integer $Q$, if $P^2 + 17^Q = 10^8$, determine how many integer values $P$ can take.",
"role": "user"
}
] | 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... | $1,136,858 |
[
{
"content": "Calculate the finite value of \\(E(|X-Y|)\\) where \\(X\\) and \\(Y\\) are independent standard uniform random variables on the interval \\([0, 1]\\).",
"role": "user"
}
] | \dfrac{1}{3} |
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