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... | 0.76 mL |
[
{
"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... | 2.453*10^{-3} J/kg |
[
{
"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... | x = -16 * 10^5 |
[
{
"content": "Consider the process $X_{t} = \\exp\\left\\{\\left(\\mu-r-\\frac{\\sigma^{2}}{2}\\right)t+\\sigma W_{t}\\right\\}$, which is the solution to the stochastic differential equation (SDE):\n\\[dX_{t}=(\\mu -r)X_t dt+\\sigma X_t d W_{t}, \\ X_{0}=1\\]\nwhere $W$ is a standard 1-dimensional Brownian mot... | 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... | P = P(X) * P(Y) |
[
{
"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... | 13065.4751 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... | $690 |
[
{
"content": "Calculate the angle between the line \\((6, 8, 5) + t (3, 4, 5)\\), where \\(t \\in \\mathbb{R}\\), and the sphere \\(x^2 + y^2 + z^2 = 25\\) at their points of intersection.",
"role": "user"
}
] | 45^\circ |
[
{
"content": "Consider the set of points \\(S\\) where each point \\((x, y)\\) has integer coordinates with \\(1 \\leq x, y \\leq 26\\). Determine the number of ways to select a convex subset of \\(S\\) that contains exactly 98 points.",
"role": "user"
}
] | 520 |
[
{
"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... | T^2 / R^3 = 1 |
[
{
"content": "Let $Y$ be a discrete random variable with probability mass function $P(Y = y)$. Determine whether the following limit exists:\n\n$$\\lim_{d_k\\downarrow d^*}P(d^*<Y\\leq d_k)$$",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the line integral \\(\\oint_C \\frac{x}{x^2 + y^2} \\,dx - \\frac{y}{x^2 + y^2} \\,dy\\) where \\(C\\) is the ellipse defined by \\(\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1.\\)",
"role": "user"
}
] | 0 |
[
{
"content": "If $\\alpha_i, i=0,1,2,...,n-1$ are the nth roots of unity, evaluate the sum $\\sum_{i=0}^{n-1} \\frac{\\alpha_i}{3-\\alpha_i}$. Choose the correct answer from the following options:\n\nA) $\\frac{n}{3^n-1}$\n\nB) $\\frac{n-1}{3^n-1}$\n\nC) $\\frac{n+1}{3^n-1}$\n\nD) $\\frac{n+2}{3^n-1}$",
"ro... | A |
[
{
"content": "For a matrix with linearly independent columns, determine if it is possible to find a matrix that acts as a left inverse, even if the linear transformation associated with the matrix is not defined on the entire domain.",
"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... | growth in GDP deflator = growth in nominal GDP - growth in real GDP |
[
{
"content": "In triangle ABC, where AB = AC = 25 units and BC = 14 units, there is a point P inside the triangle such that the perpendicular distances from P to all three sides are equal. Find the length of this equal distance.",
"role": "user"
}
] | \dfrac{21}{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... | 40.91 |
[
{
"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... | 2.3e12 N/(C*s) |
[
{
"content": "Triangle $ABC$ has $\\angle C = 60^{\\circ}$ and $BC = 4$. Point $D$ is the midpoint of $BC$. What is the largest possible value of $\\tan{\\angle BAD}$?\n$\\mathrm{(A)}\\ \\frac{\\sqrt{3}}{6}\\qquad\\mathrm{(B)}\\ \\frac{\\sqrt{3}}{3}\\qquad\\mathrm{(C)}\\ \\frac{\\sqrt{3}}{2\\sqrt{2}}\\qquad\\ma... | \frac{\sqrt{3}}{4\sqrt{2}-3} |
[
{
"content": "Find a nontrivial solution to the initial-value problem \\( y' = ty^a \\) with \\( y(0) = 0 \\) and \\( a > 1 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Let $f : \\mathbb{R} \\to \\mathbb{R}$ be a function such that\n\\[f(xf(y) + x) = xy + f(x)\\]for all $x,$ $y.$\n\nLet $n$ be the number of possible values of $f(2),$ and let $s$ be the sum of all possible values of $f(2).$ Find $n \\times s.$",
"role": "user"
}
] | 0 |
[
{
"content": "Let nonzero complex numbers \\( x \\) and \\( y \\) satisfy \\( x^2 + xy + y^2 = 0 \\). Determine the value of the expression \\(\\left(\\frac{x}{x+y}\\right)^{1990} + \\left(\\frac{y}{x+y}\\right)^{1990}\\).",
"role": "user"
}
] | -1 |
[
{
"content": "Let $A$ be a $n \\times n$ non-singular symmetric matrix with entries in $(0,\\infty)$. Determine which of the following statements is true:\n\n(a) $|A| > 0$ (where $|A|$ denotes the determinant of $A$).\n\n(b) $A$ is a positive definite matrix.\n\n(c) $B = A^2$ is a positive definite matrix.\n\n(... | C |
[
{
"content": "Find the integer value of \\( a \\) such that the polynomial \\( x^6 - 33x + 20 \\) is divisible by \\( x^2 - x + a \\).",
"role": "user"
}
] | 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... | 982.43 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... | $23,833.33 |
[
{
"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... | 5.0e-5 g |
[
{
"content": "Let $X$ be the number of tosses of a fair coin required to get the first head. If $Y | X = n$ is distributed as $Binomial(n, 1/2)$, find $P(Y = 1)$. Express your answer as a probability.",
"role": "user"
}
] | \dfrac{4}{9} |
[
{
"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... | 8,800 units |
[
{
"content": "Let $h: S' \\rightarrow S$ be a faithfully flat quasi-compact morphism. Let $f, g: X \\rightarrow Y$ be morphisms of $S$-schemes. If the base changes $f', g'$ of $f, g$ by $h$ satisfy $f' = g'$, does it follow that $f = g$?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the smallest integer $N$ such that for all $n > N$, the inequality $|n^{1/n} - 1| < 0.1$ holds.",
"role": "user"
}
] | 38 |
[
{
"content": "Let $a, b, c, d > 0$ satisfy the following conditions: \\( (a-c)(b-d) = -4 \\) and \\( \\frac{a+c}{2} \\geq \\frac{a^2 + b^2 + c^2 + d^2}{a+b+c+d} \\). Find the minimum value of the expression \\( a+c \\).",
"role": "user"
}
] | 4\sqrt{2} |
[
{
"content": "Ramon sells two enchiladas and three tacos for $\\$$2.50 and he sells three enchiladas and two tacos for $\\$$2.70. Assuming a fixed price per item, what is the cost, in dollars, of three enchiladas and four tacos? Express your answer as a decimal to the nearest hundredth.",
"role": "user"
}... | \$3.54 |
[
{
"content": "Determine the value of $k$ such that the function \\( f(x) = \\begin{cases} \\frac{kx^3}{(1+2x)^6} & x > 0 \\\\ 0 & x \\le 0 \\end{cases} \\) is a valid probability density function.",
"role": "user"
}
] | 320 |
[
{
"content": "In a rectangular parallelepiped \\( ABCD A_{1} B_{1} C_{1} D_{1} \\), the edge lengths are \\( AB = 42 \\), \\( AD = 126 \\), and \\( AA_{1} = 42 \\). Point \\( E \\) is the midpoint of edge \\( A_{1}B_{1} \\), and point \\( F \\) is the midpoint of edge \\( B_{1}C_{1} \\). Calculate the distance ... | 36 |
[
{
"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... | 1.008 N/C |
[
{
"content": "The number 4641 can be expressed as the product of two 2-digit whole numbers. What is the sum of these two numbers?",
"role": "user"
}
] | 142 |
[
{
"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... | 2000 |
[
{
"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... | 1.40e+24 atoms |
[
{
"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 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... | 5.04e-3 Wb |
[
{
"content": "Let $A$ be a real $3 \\times 3$ matrix such that $A^3 = I$ and $A \\neq I$. Determine the trace of $A$. \\( \\text{(The trace of a matrix is the sum of its diagonal elements.)} \\)",
"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... | 74.3 m |
[
{
"content": "Evaluate the integral \\( I = \\int_{0}^{\\pi} \\sin(x)\\cos(x)\\cos(2x)\\cos(4x)\\cdots \\cos(2^{n-1}x) \\, \\mathrm{d}x \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Consider the wave equation given by:\n\\[ \\partial_t^2 u(t,x) - \\partial_x^2 u(t,x) = 0 \\]\nwith initial conditions:\n\\[ u(0,x) = g(x) \\]\n\\[ \\partial_t u(0,x) = h(x) \\]\nIf both \\(g(x)\\) and \\(h(x)\\) are monotone increasing functions, is it true that the solution \\(u(t,x)\\) is also ... | Yes |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to+\\infty}\\ln(5^x-x^2)\\left[\\ln(x^6+1)-3\\ln(x^3-x)\\right].$$",
"role": "user"
}
] | -\infty |
[
{
"content": "Determine whether a smooth 1-manifold can be covered using only three coordinate patches. Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Find the sum of the series \\( \\sum_{n=1}^{\\infty} \\frac{1}{3^n} \\cdot \\cos^2\\left(\\frac{2 n \\pi}{3}\\right) \\).",
"role": "user"
}
] | \dfrac{2}{13} |
[
{
"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... | 79.9 g Cl |
[
{
"content": "Given symmetric positive definite matrices $A$ and $B$ in $\nabla{R}^{n \\times n}$ such that \\( \\| Ax \\| \\leq \\| Bx \\| \\) for every $x \\in \\nabla{R}^n$, do the eigenvalues satisfy \\( \\lambda_i(A) \\leq \\lambda_i(B) \\) for all $i$, where \\( \\lambda_i(A) \\) and \\( \\lambda_i(B) \\)... | Yes |
[
{
"content": "Suppose $X$ is a locally compact metric space which is $\\sigma$-compact, and let $K$ be a compact subset of $X$. Consider a sequence of compact sets $K_{n}$ such that $K_{n} \\subset \\textrm{int}(K_{n + 1})$ and $X = \\bigcup_{n = 1}^{\\infty}K_{n}$. Must there exist an integer $N$ such that $K ... | 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... | 9.0e-4 M |
[
{
"content": "Suppose that $f:\\mathbb{R}^n\\to [0,\\infty)$ is a function that can be written in the form \\[f(x_1,\\dots,x_n)=g_1(x_1)+g_2(x_2)+\\dots+g_n(x_n).\\] Is it possible to choose all functions $g_k$ to be nonnegative?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the number of decimal digits in the number \\(2^{3021377}\\).",
"role": "user"
}
] | 909526 |
[
{
"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... | 6.43% |
[
{
"content": "What is the largest $2$-digit prime factor of the integer $n = {200\\choose 100}$?",
"role": "user"
}
] | 61 |
[
{
"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... | 25062.04 |
[
{
"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... | $56.56 |
[
{
"content": "In triangle \\(ABC\\), points \\(C_{1}\\), \\(B_{1}\\), and \\(A_{1}\\) are located on sides \\(AB\\), \\(AC\\), and \\(CB\\), respectively, such that\n\n\\[ \\frac{AC_{1}}{C_{1}B} = \\frac{BA_{1}}{A_{1}C} = \\frac{CB_{1}}{B_{1}A} = \\lambda \\]\n\nLet the radii of the incircles of triangles \\(AC... | 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... | 44.5 |
[
{
"content": "Find $4^{-1} \\pmod{35}$, as a residue modulo 35. (Give an answer between 0 and 34, inclusive.)",
"role": "user"
}
] | 9 |
[
{
"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... | 70 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... | 1.40e-3 N |
[
{
"content": "Consider the Prokhorov metric $d_P$ on the space of probability measures on $\\mathbb{R}$, defined as \\[d_P (\\mu , \\nu ) := \\inf \\{ \\varepsilon > 0 : \\mu (B) \\leq \\nu (B^\\varepsilon) + \\varepsilon \\text{ for all Borel sets } B \\},\\] where $B^\\varepsilon := \\{ x\\in \\mathbb{R} : \\... | Yes |
[
{
"content": "In a triangle, the perimeter and the area have the same numerical value when measured in a certain unit. If the lengths of the three altitudes of the triangle are \\( p, q, \\) and \\( r \\), find the numerical value of \\( \\frac{1}{q} + \\frac{1}{p} + \\frac{1}{r} \\).",
"role": "user"
}
] | \dfrac{1}{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... | Imperfect Market
Prevention Resale of the products.
Existence of different market segments. |
[
{
"content": "A diagnostic test for a disease has a 95% chance of returning a true positive and a 10% chance of a false positive. The true proportion of diseased individuals in the population is \\(d\\). Everyone is screened, and those who test positive are tested again. Of these, 25% test positive on the secon... | \dfrac{3}{136} |
[
{
"content": "Determine the number of positive roots for the equation \\(e^{2x} - \\ln(2x) - 2^{2015} = 0\\) using the concept of concavity.",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the limit \\( \\lim_{t\\to \\infty} f(t) \\), where \\( f(t) = \\int_{0}^{\\infty} e^{-tx} \\frac{\\sin x}{x} \\, dx \\). Consider how the Dominated Convergence Theorem might be applied in this context.",
"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... | 43.32 kg - 69.31 kg |
[
{
"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... | $37.33 |
[
{
"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... | $5,263.16 |
[
{
"content": "Determine whether the rank of a positive semi-definite operator is equal to the rank of its square root.",
"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... | $3,067.9826 |
[
{
"content": "In quadrilateral $ABCD$, the diagonals $AC$ and $BD$ are equal and intersect at point $O$. The perpendicular bisectors of segments $AB$ and $CD$ intersect at point $P$, and the perpendicular bisectors of segments $BC$ and $AD$ intersect at point $Q$. Determine the measure of angle $\\angle POQ$. "... | 90^\circ |
[
{
"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... | 4.59*10^6 revolutions |
[
{
"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... | 28.4 degrees Celcius |
[
{
"content": "Let $q(z)$ be a rational function where the degree of the denominator exceeds that of the numerator by $l$, with $l \\geq 2$. Prove that \\( \\sum_{c \\in \\mathbb{C}} \\operatorname{Res}_{c} q = 0 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Find the derivative of the integral \\( \\int_{-\\infty}^\\infty f(x)g(x)\\,dx \\) with respect to the function \\( g(x) \\).",
"role": "user"
}
] | f(x) |
[
{
"content": "Identify the Lie group $G$ corresponding to the Lie algebra:\n\n$$\\text{Lie}(G)=\\left\\{\\begin{bmatrix}0 & a & u\\\\ -a & 0 & v\\\\0&0&0\\end{bmatrix}; a,u,v\\in\\mathbb{R}\\right\\}$$",
"role": "user"
}
] | SE(2) |
[
{
"content": "The function $f(x)$ satisfies\n\\[f(x + y) = f(x) + f(y) + 2xy\\]for all real numbers $x$ and $y.$ If $f(1) = 4,$ then find $f(8).$",
"role": "user"
}
] | 88 |
[
{
"content": "Estimate \\( \\int_0^1 \\sin(x^2) \\, dx \\) using the Taylor expansion of \\( \\sin(x) \\) such that the error is less than 0.00002. First, find the Taylor polynomial \\( T_6(x) \\) for \\( f(x) = \\sin(x) \\) about \\( x=0 \\). Then, use this polynomial to approximate the integral and ensure the... | 0.31028 |
[
{
"content": "Determine the values of \\(a\\) for which the matrix \\(A = \\begin{pmatrix} 2 & 0 & 0 \\\\ a & 2 & 0 \\\\ a+3 & a & -1 \\end{pmatrix}\\) can be diagonalized.",
"role": "user"
}
] | 0 |
[
{
"content": "A convex pentagon has interior angles with measures $x+1$, $2x$, $3x$, $4x$, and $5x-1$ degrees. What is the measure of the largest angle?",
"role": "user"
}
] | 179 |
[
{
"content": "Evaluate the integral \\[ I = \\int_{0}^{1} \\int_{0}^{1} \\int_{0}^{1} \\int_{0}^{1} \\int_{0}^{1} \\int_{0}^{1} \\delta(x_1-x_2+x_3-x_4)\\delta(x_2-x_3+x_5-x_6) \\, dx_1 \\, dx_2 \\, dx_3 \\, dx_4 \\, dx_5 \\, dx_6. \\]",
"role": "user"
}
] | \dfrac{1}{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... | 1.088 |
[
{
"content": "Determine the range of values for the real number \\( a \\) such that the function \\( f(x) = x^2 - 2x - |x - 1 - a| - |x - 2| + 4 \\) is always non-negative for any real number \\( x \\).",
"role": "user"
}
] | [-2, 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... | $500 billion increase in money supply |
[
{
"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... | $2,250,000 |
[
{
"content": "Find the determinant of the principal matrix solution \\( \\Pi(t,t_0) \\) for the system of differential equations \\( \\dot{x} = A(t)x \\) in \\( \\mathbb{R}^2 \\), where the matrix \\( A(t) \\in GL(\\mathbb{R}^2) \\) has eigenvalues \\( \\alpha_1(t) = t \\) and \\( \\alpha_2(t) = 0 \\). Calculat... | \sqrt{e} |
[
{
"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... | 2.13 V |
[
{
"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... | 0.544 eV |
[
{
"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... | mild |
[
{
"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... | 1.24e7 N |
[
{
"content": "You toss a fair coin one million times. What is the probability of obtaining at least one sequence of six consecutive heads followed by six consecutive tails?",
"role": "user"
}
] | 1 |
[
{
"content": "Determine the ratio of the circumference to the diameter of a circle on a sphere, given that the circle is defined by an angle \\( \\theta \\) from the pole. The radius of the sphere is \\( r \\). Express the ratio \\( R(\\theta) \\) in terms of \\( \\theta \\).",
"role": "user"
}
] | \dfrac{\pi \sin \theta}{\theta} |
[
{
"content": "Does there exist a subsequence \\(\\{x_{n_k}\\}\\) of a positive real sequence \\(\\{x_n\\}\\) such that \\(x_{n_k} > x\\) if \\(\\limsup_n x_n > x\\)?",
"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... | 7.717e-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... | 3684 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... | 0.20 kg |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.