prompt listlengths 2 2 | adversarial bool 1
class | source stringclasses 1
value | conv_id stringlengths 6 8 | unique_conv_id stringlengths 11 13 | turn_id int64 1 1 | data_source stringclasses 1
value | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|---|---|---|---|---|
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_0 | uniq_conv_0 | 1 | minerva | minerva | {
"ground_truth": "1.6",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Each of the two Magellan telescopes has a diameter of $6.5 \\mathrm{~m}$. In one configuration the effective focal length is $72 \\mathrm{~m}$. Find the diameter of the image of a planet (in $\\mathrm{cm}$ ) at this focus if the angular diameter of t... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_1 | uniq_conv_1 | 1 | minerva | minerva | {
"ground_truth": "4.5e33",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A white dwarf star has an effective temperature, $T_{e}=50,000$ degrees Kelvin, but its radius, $R_{\\mathrm{WD}}$, is comparable to that of the Earth. Take $R_{\\mathrm{WD}}=10^{4} \\mathrm{~km}\\left(10^{7} \\mathrm{~m}\\right.$ or $\\left.10^{9} \... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_2 | uniq_conv_2 | 1 | minerva | minerva | {
"ground_truth": "41.8",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A prism is constructed from glass and has sides that form a right triangle with the other two angles equal to $45^{\\circ}$. The sides are $L, L$, and $H$, where $L$ is a leg and $H$ is the hypotenuse. A parallel light beam enters side $L$ ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_3 | uniq_conv_3 | 1 | minerva | minerva | {
"ground_truth": "20.39",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A particular star has an absolute magnitude $M=-7$. If this star is observed in a galaxy that is at a distance of $3 \\mathrm{Mpc}$, what will its apparent magnitude be?",
"role": "user"
}
],
"index": 3,
"single_turn_completion": "20.... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_4 | uniq_conv_4 | 1 | minerva | minerva | {
"ground_truth": "0.006",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find the gravitational acceleration due to the Sun at the location of the Earth's orbit (i.e., at a distance of $1 \\mathrm{AU}$ ). Give your answer in meters per second squared, and express it to one significant figure.",
"role": "user"
}... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_5 | uniq_conv_5 | 1 | minerva | minerva | {
"ground_truth": "np.arcsin(10/13)",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A collimated light beam propagating in water is incident on the surface (air/water interface) at an angle $\\theta_w$ with respect to the surface normal.\n\nSubproblem 0: If the index of refraction of water is $n=1.3$, find an expression fo... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_6 | uniq_conv_6 | 1 | minerva | minerva | {
"ground_truth": "0.49",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find the theoretical limiting angular resolution (in arcsec) of a commercial 8-inch (diameter) optical telescope being used in the visible spectrum (at $\\lambda=5000 \\AA=500 \\mathrm{~nm}=5 \\times 10^{-5} \\mathrm{~cm}=5 \\times 10^{-7} \\mathrm{~... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_7 | uniq_conv_7 | 1 | minerva | minerva | {
"ground_truth": "100",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A star has a measured parallax of $0.01^{\\prime \\prime}$, that is, $0.01$ arcseconds. How far away is it, in parsecs?",
"role": "user"
}
],
"index": 7,
"single_turn_completion": "100",
"single_turn_prompt": "A star has a measured ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_8 | uniq_conv_8 | 1 | minerva | minerva | {
"ground_truth": "0.022",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "An extrasolar planet has been observed which passes in front of (i.e., transits) its parent star. If the planet is dark (i.e., contributes essentially no light of its own) and has a surface area that is $2 \\%$ of that of its parent star, find the de... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_9 | uniq_conv_9 | 1 | minerva | minerva | {
"ground_truth": "9.6",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "If the Bohr energy levels scale as $Z^{2}$, where $Z$ is the atomic number of the atom (i.e., the charge on the nucleus), estimate the wavelength of a photon that results from a transition from $n=3$ to $n=2$ in Fe, which has $Z=26$. Assume that the ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_10 | uniq_conv_10 | 1 | minerva | minerva | {
"ground_truth": "3.83e35",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "If the Sun's absolute magnitude is $+5$, find the luminosity of a star of magnitude $0$ in ergs/s. A useful constant: the luminosity of the sun is $3.83 \\times 10^{33}$ ergs/s.",
"role": "user"
}
],
"index": 10,
"single_turn_completi... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_11 | uniq_conv_11 | 1 | minerva | minerva | {
"ground_truth": "300",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A spectrum is taken of a single star (i.e., one not in a binary). Among the observed spectral lines is one from oxygen whose rest wavelength is $5007 \\AA$. The Doppler shifted oxygen line from this star is observed to be at a wavelength of... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_12 | uniq_conv_12 | 1 | minerva | minerva | {
"ground_truth": "\\frac{2 \\pi c^{2} R^{2}}{\\lambda^{5}\\left[e^{h c /(\\lambda k T)}-1\\right] d^{2}}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "The differential luminosity from a star, $\\Delta L$, with an approximate blackbody spectrum, is given by:\n\\[\n\\Delta L=\\frac{8 \\pi^{2} c^{2} R^{2}}{\\lambda^{5}\\left[e^{h c /(\\lambda k T)}-1\\right]} \\Delta \\lambda\n\\]\nwhere $R$ is the ra... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_13 | uniq_conv_13 | 1 | minerva | minerva | {
"ground_truth": "8.7e8",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A very hot star is detected in the galaxy M31 located at a distance of $800 \\mathrm{kpc}$. The star has a temperature $T = 6 \\times 10^{5} K$ and produces a flux of $10^{-12} \\mathrm{erg} \\cdot \\mathrm{s}^{-1} \\mathrm{cm}^{-2}$ at the... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_14 | uniq_conv_14 | 1 | minerva | minerva | {
"ground_truth": "0.003",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A star is at a distance from the Earth of $300 \\mathrm{pc}$. Find its parallax angle, $\\pi$, in arcseconds to one significant figure.",
"role": "user"
}
],
"index": 14,
"single_turn_completion": "0.003",
"single_turn_prompt": "A s... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_15 | uniq_conv_15 | 1 | minerva | minerva | {
"ground_truth": "4e33",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "The Sun's effective temperature, $T_{e}$, is 5800 Kelvin, and its radius is $7 \\times 10^{10} \\mathrm{~cm}\\left(7 \\times 10^{8}\\right.$ m). Compute the luminosity (power output) of the Sun in erg/s. Treat the Sun as a blackbody radiator, and giv... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_16 | uniq_conv_16 | 1 | minerva | minerva | {
"ground_truth": "4.49",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Use the Bohr model of the atom to compute the wavelength of the transition from the $n=100$ to $n=99$ levels, in centimeters. [Uscful relation: the wavelength of $L \\alpha$ ( $\\mathrm{n}=2$ to $\\mathrm{n}=1$ transition) is $1216 \\AA$.]",
"r... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_17 | uniq_conv_17 | 1 | minerva | minerva | {
"ground_truth": "0.01",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A radio interferometer, operating at a wavelength of $1 \\mathrm{~cm}$, consists of 100 small dishes, each $1 \\mathrm{~m}$ in diameter, distributed randomly within a $1 \\mathrm{~km}$ diameter circle. \n\nWhat is the angular resolution of ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_18 | uniq_conv_18 | 1 | minerva | minerva | {
"ground_truth": "3.3e12",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: Orbital Dynamics: A binary system consists of two stars in circular orbit about a common center of mass, with an orbital period, $P_{\\text {orb }}=10$ days. Star 1 is observed in the visible band, and Doppler measurements show that its orb... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_19 | uniq_conv_19 | 1 | minerva | minerva | {
"ground_truth": "10",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "If a star cluster is made up of $10^{4}$ stars, each of whose absolute magnitude is $-5$, compute the combined apparent magnitude of the cluster if it is located at a distance of $1 \\mathrm{Mpc}$.",
"role": "user"
}
],
"index": 19,
"... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_20 | uniq_conv_20 | 1 | minerva | minerva | {
"ground_truth": "6630",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A galaxy moves directly away from us with a speed of $3000 \\mathrm{~km} \\mathrm{~s}^{-1}$. Find the wavelength of the $\\mathrm{H} \\alpha$ line observed at the Earth, in Angstroms. The rest wavelength of $\\mathrm{H} \\alpha$ is $6565 \\AA$. Take... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_21 | uniq_conv_21 | 1 | minerva | minerva | {
"ground_truth": "1.2",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "The Spitzer Space Telescope has an effective diameter of $85 \\mathrm{cm}$, and a typical wavelength used for observation of $5 \\mu \\mathrm{m}$, or 5 microns. Based on this information, compute an estimate for the angular resolution of the Spitzer ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_22 | uniq_conv_22 | 1 | minerva | minerva | {
"ground_truth": "3e6",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "It has long been suspected that there is a massive black hole near the center of our Galaxy. Recently, a group of astronmers determined the parameters of a star that is orbiting the suspected black hole. The orbital period is 15 years, and the orbita... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_23 | uniq_conv_23 | 1 | minerva | minerva | {
"ground_truth": "7e37",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A very hot star is detected in the galaxy M31 located at a distance of $800 \\mathrm{kpc}$. The star has a temperature $T = 6 \\times 10^{5} K$ and produces a flux of $10^{-12} \\mathrm{erg} \\cdot \\mathrm{s}^{-1} \\mathrm{cm}^{-2}$ at the... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_24 | uniq_conv_24 | 1 | minerva | minerva | {
"ground_truth": "50",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A large ground-based telescope has an effective focal length of 10 meters. Two astronomical objects are separated by 1 arc second in the sky. How far apart will the two corresponding images be in the focal plane, in microns?",
"role": "user"
... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_25 | uniq_conv_25 | 1 | minerva | minerva | {
"ground_truth": "\\frac{a M^{1 / 3}}{G M^{2 / 3}+b}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "The equation of state for cold (non-relativistic) matter may be approximated as:\n\\[\nP=a \\rho^{5 / 3}-b \\rho^{4 / 3}\n\\]\nwhere $P$ is the pressure, $\\rho$ the density, and $a$ and $b$ are fixed constants. Use a dimensional analysis of the equa... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_26 | uniq_conv_26 | 1 | minerva | minerva | {
"ground_truth": "7.5e7",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Take the total energy (potential plus thermal) of the Sun to be given by the simple expression:\n\\[\nE \\simeq-\\frac{G M^{2}}{R}\n\\]\nwhere $M$ and $R$ are the mass and radius, respectively. Suppose that the energy generation in the Sun were sudde... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_27 | uniq_conv_27 | 1 | minerva | minerva | {
"ground_truth": "\\frac{dM}{dt}=\\frac{10^{5} L_{\\odot}}{0.007 c^{2} M_{\\odot}^{6}} M^{6}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: Once a star like the Sun starts to ascend the giant branch its luminosity, to a good approximation, is given by:\n\\[\nL=\\frac{10^{5} L_{\\odot}}{M_{\\odot}^{6}} M_{\\text {core }}^{6}\n\\]\nwhere the symbol $\\odot$ stands for the solar v... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_28 | uniq_conv_28 | 1 | minerva | minerva | {
"ground_truth": "\\left[P_{0}^{2 / 5}-\\frac{2}{5} g K^{-3 / 5} z\\right]^{5 / 2}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A star of radius, $R$, and mass, $M$, has an atmosphere that obeys a polytropic equation of state:\n\\[\nP=K \\rho^{5 / 3} \\text {, }\n\\]\nwhere $P$ is the gas pressure, $\\rho$ is the gas density (mass per unit volume), and $K$ is a constant throu... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_29 | uniq_conv_29 | 1 | minerva | minerva | {
"ground_truth": "1.75",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "An eclipsing binary consists of two stars of different radii and effective temperatures. Star 1 has radius $R_{1}$ and $T_{1}$, and Star 2 has $R_{2}=0.5 R_{1}$ and $T_{2}=2 T_{1}$. Find the change in bolometric magnitude of the binary, $\\Delta m_{\... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_30 | uniq_conv_30 | 1 | minerva | minerva | {
"ground_truth": "\\sqrt{4 \\pi G \\rho_{0} r_{0}^{2}}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: It has been suggested that our Galaxy has a spherically symmetric dark-matter halo with a density distribution, $\\rho_{\\text {dark }}(r)$, given by:\n\\[\n\\rho_{\\text {dark }}(r)=\\rho_{0}\\left(\\frac{r_{0}}{r}\\right)^{2},\n\\]\nwhere... |
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