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... | 0.8 m/s |
[
{
"content": "Evaluate the integral \\( \\int_{(-1, 1)} |x| \\, d\\mu \\), where \\( \\mu((a, b]) = \\int_a^b \\frac{1}{1+x^2} \\, dx \\) for all intervals \\((a, b]\\) on the measurable space \\((\\mathbb{R}, \\mathcal{B})\\).",
"role": "user"
}
] | \ln 2 |
[
{
"content": "If $1+2x+3x^2 + \\dotsb=9$, find $x$.",
"role": "user"
}
] | \frac{2}{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... | 13 mV |
[
{
"content": "175 schoolchildren arrived at a health camp. Some children know each other, and some do not. It is known that any six schoolchildren can be accommodated in two three-person rooms such that all the schoolchildren in one room will know each other. What is the minimum number of pairs of acquainted sc... | 7569 |
[
{
"content": "Consider the curve \\( y = x^4 + Ax^3 + Bx^2 + Cx + D \\) which touches the line \\( y = px + q \\) at \\( x = 2 \\) and \\( x = 3 \\), where \\( A, B, C, D, p, q \\in \\mathbb{R} \\). If the area bounded by the curve and the line is \\( \\frac{1}{\\alpha} \\), find the number of divisors of \\( \... | 8 |
[
{
"content": "The three roots of the cubic $ 30 x^3 - 50x^2 + 22x - 1$ are distinct real numbers strictly between $ 0$ and $ 1$. If the roots are $p$, $q$, and $r$, what is the sum\n\\[ \\frac{1}{1-p} + \\frac{1}{1-q} +\\frac{1}{1-r} ?\\]",
"role": "user"
}
] | 12 |
[
{
"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... | 600 m/s |
[
{
"content": "Consider a grid of points \\((x, y)\\) where both \\(x\\) and \\(y\\) are positive integers less than or equal to 6. A *magic grid* is an assignment of an integer to each point in this grid such that for every square with horizontal and vertical sides and all four vertices in the grid, the sum of ... | 2^{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... | 1.221 g |
[
{
"content": "Let $k$ be a field and $A$ a finite-dimensional commutative $k$-algebra. Suppose a finite group $G$ acts on $A$ by automorphisms, and $A^G = \\{a \\in A \\mid ga = g \\text{ for any } g \\in G \\}$ is isomorphic to $k$. Is the action of $G$ on $\\operatorname{Spec}(A)$ transitive under these assum... | 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... | 555.6 V |
[
{
"content": "What are all values of $p$ such that for every $q>0$, we have $$\\frac{3(pq^2+p^2q+3q^2+3pq)}{p+q}>2p^2q?$$ Express your answer in interval notation in decimal form.",
"role": "user"
}
] | [0,3) |
[
{
"content": "Determine whether the following statement is true or false: If a function $f$ is analytic in a simply connected domain $D$, then the contour integral of $f$ over any closed loop within $D$ is zero.",
"role": "user"
}
] | A |
[
{
"content": "Evaluate the limit: $$ \\lim_{x \\to\\infty} \\frac{\\log\\log x }{ \\sqrt{\\log x}}. $$",
"role": "user"
}
] | 0 |
[
{
"content": "Find the last 5 digits of the sum: \\(1! + 2\\cdot 2! + \\cdots + 24 \\cdot 24!\\).",
"role": "user"
}
] | 99999 |
[
{
"content": "In a party with \\( n + 1 \\) couples, where handshakes between spouses are forbidden, a total of \\( 2n + 1 \\) guests (excluding the host and hostess) report \\( 2n + 1 \\) unique numbers of handshakes. Determine the number of handshakes the host made.",
"role": "user"
}
] | 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... | 4.55 |
[
{
"content": "Consider the infinite strip \\(S= \\{x \\in \\mathbb{R}^3 : a < x_1 < b \\} \\) in three-dimensional Euclidean space. Determine whether the only \\(L^2\\) harmonic function in this strip is the zero function.",
"role": "user"
}
] | 0 |
[
{
"content": "Given the transition probability matrix \\( P = \\begin{bmatrix} 1 & 0.1 & 0.8 \\\\ 0 & 0.7 & 0.2 \\\\ 0 & 0.2 & 0 \\end{bmatrix} \\) and the initial state \\( s_0 = \\begin{bmatrix} 0 \\\\ 0 \\\\ 1 \\end{bmatrix} \\), calculate the expected number of steps needed for absorption.",
"role": "us... | \dfrac{25}{13} |
[
{
"content": "Let \\( A = k[x,y] \\) where \\( k \\) is an algebraically closed field, and let \\( M = A/(xy) \\) be an \\( A \\)-module. Calculate the support of \\( M \\), denoted as \\( \\text{Supp}(M) = \\{ P \\in \\text{Spec}(A) : M_P \\neq 0 \\} \\), where \\( M_P = S^{-1}M \\) and \\( S = A \\setminus P ... | V(x) \cup V(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... | 2.04 m |
[
{
"content": "Given a sequence of complex numbers $(a_n)_{n\\ge 0}$ such that $\\lim_{n\\to \\infty} a_n=L\\neq 0$, evaluate the limit: $$\\lim_{x\\to 1^-} (1-x)\\sum_{n\\ge 0} a_n x^n.$$",
"role": "user"
}
] | L |
[
{
"content": "Determine the number of vectors \\(\\lambda=(\\lambda_1,\\ldots,\\lambda_n)\\in\\mathbb{N}^n_{\\geq0}\\) that satisfy the following conditions:\n\n1. \\(\\lambda_1 = \\lambda_2 = \\cdots = \\lambda_{k-1} = \\lambda_k < \\lambda_{k+1} < \\cdots < \\lambda_{n-1} < \\lambda_n \\leq n\\)\n2. \\(k \\in... | 2^{n+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... | Sales Revenue: $54,000
Direct Labor: $8,100
Materials: $7,560
Variable Overhead: $5,400
Marketing: $3,240
Administrative: $2,700
Total Variable Costs: $27,000
Contribution Margin: $27,000
Manufacturing Fixed Costs: $3,000
Marketing Fixed Costs: $6,000
Administrative Fixed Costs: $6,000
Total Fixed Costs: $15,000
Operat... |
[
{
"content": "Determine the order of the zero at \\(z=0\\) for the function \\(f(z)=\\frac{z^{3}}{1+z -e^{z}}\\), given the expansion of \\(e^z\\) as \\(1+z+\\frac{z^2}{2!}+\\frac{z^3}{3!}+\\cdots\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Given a graph where each node has at most $e$ edges and the shortest distance between any two nodes is at most $d$, determine the maximum number of nodes $M$ the graph can have. For instance, if $(e,d) = (2,6)$, then $M = 13$. Find $M$ for the case where $(e,d) = (3,2)$. Provide your answer as a s... | 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... | 3.98 * 10^6 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... | 5 atm or 5e5 Pa |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty}\\frac{\\sin(t)}{t}f(t)dt \\) given that the Fourier transform of \\( f \\) is \\( \\hat{f}(w)=\\frac{w}{1+w^4} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "For the special orthogonal group $SO(3)$, is the adjoint representation the same as the fundamental representation?",
"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... | 2.32e-2 |
[
{
"content": "What is the remainder when the base 4 number $120301232_4$ is divided by 8? Express your answer in base 10.",
"role": "user"
}
] | 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... | 37.0 m/s at an angle of 6.18 degrees below the horizontal |
[
{
"content": "Determine the radius of convergence for the power series \\( \\sum _{n=1} ^{\\infty} \\frac{n!}{n^n} x^{2n} \\).",
"role": "user"
}
] | \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... | M^-3 s^-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... | 56.5 g |
[
{
"content": "Consider the nonlinear oscillator described by the differential equation \\( \\frac{d^2 u}{dt^2} + u = |u|^{p-1}u \\) for \\( p > 1 \\), where the solution \\( u(t) \\) blows up at time \\( T > 0 \\), i.e., \\( \\lim_{t \\nearrow T} u(t) = +\\infty \\). The energy associated with this system is gi... | 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... | 0.432 m/s |
[
{
"content": "Verify whether the plane given by the equation \\(x + 2y + 3z = 6\\) is tangent to the surface defined by \\(x^2 + 2y^2 + 3z^2 = 6\\) at any point.",
"role": "user"
}
] | (1, 1, 1) |
[
{
"content": "Determine whether the image of a Lebesgue measurable set under a continuous linear function from \\(\\mathbb{R}^n\\) to \\(\\mathbb{R}^n\\) is also Lebesgue measurable.",
"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... | 0.022 moles HCl/L gastric juice |
[
{
"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... | 0.0682 or 6.82% |
[
{
"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... | 1.0e+2 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... | 1.58 |
[
{
"content": "In triangle $\\triangle ABC$, the angle bisectors $BD$ and $CE$ of angles $\\angle B$ and $\\angle C$ are equal in length. Prove that $AB = AC$. ",
"role": "user"
}
] | AB = AC |
[
{
"content": "Determine the value of \\( k \\) for which the functional \\[ \\int_0^1 (y^{\\prime 2} + (y + 2y')y'' + kxyy' + y^2) ~dx, \\] with boundary conditions \\( y(0) = 0, \\ y(1) = 1, \\ y'(0) = 2, \\ y'(1) = 3 \\), is path independent. Choose the correct value of \\( k \\) from the following options:\n... | B |
[
{
"content": "Simplify the expression \\(\\tanh^{-1}(3i)\\) to the form \\(i\\tan^{-1}(3)\\). Given that \\(\\tanh^{-1}(z)=\\frac{1}{2} \\log{\\frac{1+z}{1-z}}\\), find all the complex values associated with \\(\\tanh^{-1}(3i)\\).",
"role": "user"
}
] | i \tan^{-1}(3) + i\pi k |
[
{
"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... | 7662.59 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... | 16.4 KJ/Kg |
[
{
"content": "What is the limit, as \\( n \\to \\infty \\), of the expected distance between two points chosen uniformly at random within a unit-radius hypersphere in \\( \\mathbb{R}^n \\)?",
"role": "user"
}
] | \sqrt{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... | 9.41% |
[
{
"content": "Let $U\\subseteq\\mathbb{R}^n$ and $V\\subseteq\\mathbb{R}^m$ be open sets, and consider functions $f:U\\to\\mathbb{R}$ and $g_1, g_2, \\dots, g_n:V\\to\\mathbb{R}$ such that $(g_1(x), g_2(x), \\dots, g_n(x)) \\in U$ for all $x \\in V$. Given $x_0 \\in V$ and $j \\in \\{1, \\dots, n\\}$, if $f$ is... | 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... | The dividend payable on common stock is $188,000, and the dividend payable on preferred stock is $12,000. |
[
{
"content": "Calculate the moment of inertia with respect to the $z$-axis for the surface $S$, which is the boundary of the upper half of the solid cone defined by $x^2 + y^2 < z^2 < 2$ in the $xyz$-space. Assume the surface has a constant density of $3$. Provide your answer as a single numerical value.",
... | 6\pi(1 + \sqrt{2}) |
[
{
"content": "Determine whether there exists an uncountable subset of real numbers that forms a proper subfield of \\(\\mathbf{R}\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Find the smallest positive integer \\( n \\) such that:\n\\[ 1,000,000^{{1,000,000}^{1,000,000}} < n^{n^{n^n}} \\]",
"role": "user"
}
] | 8 |
[
{
"content": "Given distinct quadratic polynomials \\( f(x) \\) and \\( g(x) \\), both with leading coefficients equal to one, it is known that \\( f(1) + f(10) + f(100) = g(1) + g(10) + g(100) \\). Find the value of \\( x \\) for which \\( f(x) = g(x) \\).",
"role": "user"
}
] | 37 |
[
{
"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... | 2.37 grams |
[
{
"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... | 2700 J |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0^+}\\cfrac{x^{x^x}}{x}.$$",
"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... | $29.27 |
[
{
"content": "Find the values of $x \\in (0, 1)$ for which the series \\( \\sum_{k=1}^{\\infty} \\frac{\\cos(2\\pi kx)}{k^2} \\) converges.",
"role": "user"
}
] | (0, 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... | 14.61 |
[
{
"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... | 3.02 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... | 0.459 bar |
[
{
"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... | 0.735 m/s |
[
{
"content": "What is the probability that the determinant of a 2x2 matrix, whose elements are independent and uniformly distributed random variables in the interval (0,1), is positive?",
"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... | $981,075.42 |
[
{
"content": "Find the multiplicative inverse of \\(2^{2000}\\) modulo \\(2017\\) using Euler's criterion.",
"role": "user"
}
] | 992 |
[
{
"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... | K = (k1*k2)/(k1+k2) |
[
{
"content": "Find the matrix that corresponds to reflecting over the vector $\\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix}.$",
"role": "user"
}
] | \begin{pmatrix} 5/13 & 12/13 \\ 12/13 & -5/13 \end{pmatrix} |
[
{
"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... | C6H8O7(aq) + 3NaHCO3(aq) -> Na3C6H5O7(aq) + 3CO2(g) + 3H2O(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... | _{15}^{244}\textrm{Y} |
[
{
"content": "Five people are sitting at a round table. Let $f\\geq 0$ be the number of people sitting next to at least 1 female and $m\\geq0$ be the number of people sitting next to at least one male. The number of possible ordered pairs $(f,m)$ is\n$\\mathrm{(A) \\ 7 } \\qquad \\mathrm{(B) \\ 8 } \\qquad \\ma... | 8 |
[
{
"content": "Let $k$ be an algebraically closed field, and consider an integral $k$-algebra $R$ of finite type. Let $M$ be a finitely generated $R$-module, and $x \\in M$. If $x$ maps to zero in $M/mM$ for every maximal ideal $m$ of $R$, determine whether $x = 0$ in $M$. Provide a justification for your answer... | 0 |
[
{
"content": "Let $A \\subseteq \\mathbb{R}$ and $a \\in A$. Define $A^+ := \\{x \\in A : x > a\\}$ and let $f: A \\to \\mathbb{R}$. Assume that the right-hand derivative \\( f'(a^+) = \\lim_{x \\to a^+} \\frac{f(x) - f(a)}{x - a} \\neq \\pm \\infty \\) exists. Can we conclude that \\( f'(a^+) = c \\in \\mathbb... | Yes |
[
{
"content": "Determine the result of the tensor product \\( \\mathbb{C}(x) \\otimes_{\\mathcal{O}_{X,x}} \\mathbb{C}(x) \\), where \\( X \\) is a complex manifold with structure sheaf \\( \\mathcal{O}_X \\), and \\( \\mathbb{C}(x) \\) is the residue field at a point \\( x \\in X \\). Is this tensor product sti... | \mathbb{C}(x) |
[
{
"content": "Find the minimum value of the expression \\( \\frac{1}{2}\\sum_{k=1}^{n}a_{k}^{2}+\\frac{1}{2}\\left(\\sum_{k=1}^n a_k\\right)^2 \\) subject to the constraint \\( \\sum_{k=1}^{n}p_{k}a_{k}=0 \\) using the method of Lagrange Multipliers.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to\\infty} \\left(\\sqrt[50]{(x + 5\\times1)(x + 5\\times2)\\cdots(x +5\\times50)} - x\\right)$$",
"role": "user"
}
] | \dfrac{255}{2} |
[
{
"content": "Find the norm of the projection operator \\( P: c \\to c_0 \\) defined by \\( P(x_0,x_1,x_2,\\ldots) = (x_0-\\lim\\limits_{n\\to\\infty}x_n,x_1-\\lim\\limits_{n\\to\\infty}x_n,x_2-\\lim\\limits_{n\\to\\infty}x_n,\\ldots) \\) in the space of convergent sequences with respect to the supremum norm.",... | 2 |
[
{
"content": "If a function \\( f: S \\times S \\rightarrow S \\) is continuous, does it imply that for each \\( a \\in S \\), the map \\( f_a(b) = f(a, b) \\) is also continuous, where \\( S \\) is equipped with the product topology?",
"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 $g \\in C[0,2]$ with $g(2) = 0$. Define the operator $\\psi(g) = \\int_0^2 g(x) \\, dx$. Determine the operator norm $||\\psi||_{\\infty}$.",
"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... | 6.0 x 10^-6 volts |
[
{
"content": "Determine whether the following statement is true or false: If $a,b,c$ are infinite sets, then $|a| < |b|$ implies $|c^a| < |c^b|$. Provide a justification for your answer.",
"role": "user"
}
] | False |
[
{
"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... | $1,169 Million |
[
{
"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=2, price=16 |
[
{
"content": "Evaluate the limit: $$ \\lim_{x\\to 0^+}\\frac{x^{\\sqrt{x}}}{\\sqrt{x^x}} $$ without using L'Hôpital's rule.",
"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... | $20,486.43 |
[
{
"content": "Given a prime number \\(p\\) of the form \\(4k+1\\), determine if the integer right-angled triangle with hypotenuse \\(p\\) is unique.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the residue of the function \\( \\frac{1}{z^{100} - 1} \\) at \\( z = 1 \\).",
"role": "user"
}
] | \dfrac{1}{100} |
[
{
"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... | 3.8e+3 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... | July: 31,500
August: 46,500
September: 59,000 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to +\\infty} \\left(\\frac{(\\ln(x+1))^x}{(2x)^{x/3}}\\right) \\]",
"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... | 28 rad/s |
[
{
"content": "Determine the angle \\(\\alpha\\) such that the vectors \\((\\rho^2 + i)^{16}\\) and \\((\\rho^2 - i)^{16}\\) are aligned with the imaginary axis on the complex plane.",
"role": "user"
}
] | \dfrac{\pi}{32} |
[
{
"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... | 5.66 |
[
{
"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... | $187.5 |
[
{
"content": "The letters of the alphabet are each assigned a random integer value, and $H=10$. The value of a word comes from the sum of its letters' values. If $MATH$ is 35 points, $TEAM$ is 42 points and $MEET$ is 38 points, what is the value of $A$?",
"role": "user"
}
] | 21 |
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