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(2*3 + 3*4 + 4*5) / (10 - 5)

integrate x^2 sin^3 x dx

plot x^2+y^2<1 and y>x

harmonic conjugate x^3 - 3 x y^2

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Anchor 1

Elementary Math

Do basic arithmetic. Work with fractions, percentages and similar fundamentals. Solve place value and word problems.

Perform arithmatic operation

(2*3 + 3*4 + 4*5) / (10 - 5)

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Generate a multiplication table:

12 by 12 multiplication table

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Algebra

Find roots of and expand, factor or simplify mathematical expressions everything from polynomials to fields and groups.

Solve an equation:

x^3 - 4x^2 + 6x - 24 = 0

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Factor a polynomial:

factor 2x^5 - 19x^4 + 58x^3 - 67x^2 + 56x - 48

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Numbers

Work with various kinds of numbers. Check for membership in larger sets, such as the rationals or the transcendental numbers. Convert between bases.

Compute a decimal approximation to a specified number of digits:

pi to 1000 digits

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Convert a decimal number to another base:

219 to binary

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Units & Measures

Convert between units, examine information on different measurement devices or explore standard sizes for a variety of objects

Convert to a specified unit:

20mL in drams

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Discover how to measure different physical properties:

acceleration measuring devices

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Equation Solving

Solve equations in one or more variables both symbolically and numerically.

Solve a polynomial equation:

solve x^2 + 4x + 6 = 0

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Solve a system of linear equations:

x+y=10, x-y=4

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Dates & Times

Convert between time zones or calendar systems or explore historical events and holidays.

Convert the time in one location to another:

If it is 7pm in Moscow, what time is it in Islamabad?

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Find notable events in a specified date range:

What happened in August 1969?

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Words and Linguistics

Find and compare definitions and other properties of words or explore languages of the world.

Find anagrams of a word or phrase:

anagrams trace

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Find words matching a pattern:

_al__la__

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Word Properties

Look up definitions, synonyms, translations and other properties of a word.

Find definitions and other properties of a word:

word march

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Translate an English word into other languages:

translate beauty to Hindi

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Number Theory

Analyze integers; subsets of the integers, including the prime numbers; and related ideas.

Compute a greatest common divisor:

gcd 24, 36, 48, 60

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Generate a list of primes:

primes <= 10000

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Hobbies

From genealogy to woodworking, access useful calculators and computations to help with your hobby.

Get information about a family relationship:

second cousin once removed

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Get information on a professional sports team:

Dallas Cowboys

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Calculus and Analysis

Compute integrals, derivatives ,limits, Fourier Transform and Laplace Transform as well as analyze sums, products and series.

Compute an indefinite integral:

integrate x^2 sin^3 x dx

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Compute a Fourier transform:

Fourier transform exp(-x^2)

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Differential Equations

Solve differential equations of any order. Examine solutions and plots of the solution families. Specify initial conditions to find exact solutions.

Solve a linear ordinary differential equation:

y'' + y = 0

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Solve a nonlinear equation:

f'(t) = f(t)^2 + 1

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Trigonometry

Perform trigonometric calculations and explore properties of trigonometric functions and identities.

Solve trigonometric equation:

sin x + cos x = 1

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Do exact arithmetic with fractions:

1/4 * (4 - 1/2)

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Probability

Compute the probabilities of certain events occurring. Compute joint, disjoint or conditional probabilities and apply them to real-world situations.

Compute probabilities for a sequence of trials:

sin x + probability of 8 successes in 14 trials with p=.6x = 1

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Compute the probability of shared birthdays in a group of people:

birthday paradox 50 people

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Integral Transforms

Calculate the Fourier transform, Laplace transform and other integral transforms of functions.

Compute a Fourier transform:

Fourier transform exp(-x^2)

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Compute a Laplace transform:

LT e^t sin 2t

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Derivatives

Take the derivative of single or multivariate functions. Compute the partial derivative of expressions with more than one variable.

Compute higher derivatives:

second derivative of sin(2x)

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Compute partial derivatives:

d/dx x^2 y^4, d/dy x^2 y^4

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Physics

Perform computations using formulas from physics, the branch of science studying properties of matter and energy.

Compute mechanical work:

work F=30N, d=100m

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Analyze an RLC circuit:

RLC circuit 10ohm, 12H, 400uF

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Chemistry

Perform computations using formulas from chemistry, the branch of science studying the nature and interactions of substances.

Balance a chemical equation:

Al + O2 -> Al2O3

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Get information about a functional group:

nitrile functional group

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Plotting & Graphics

Visualize functions, equations and inequalities. Do so in 1, 2 or 3 dimensions. Make polar and parametric plots.

Plot the solution to an equation in two variables:

plot 3x^2-2xy+y^2=1

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Plot a region satisfying multiple inequalities:

plot x^2+y^2<1 and y>x

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Life Sciences

Get information about life sciences, the branch of science studying living organisms.

Get information about a human anatomical structure:

heart

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Compare genes across organisms:

homologs of CCR5 gene

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Materials

Explore properties of a range of materials from minerals to manmade alloys and plastics.

Get information about an alloy:

carbon steel

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Compare the density of two common plastics:

density of PVC vs polyethylene

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Limits

Explore the limit behavior of a function as it approaches a single point or asymptotically approaches infinity.

Compute a limit:

limit (1+1/n)^n as n->infinity

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Compute a one-sided limit:

lim x/|x| as x->0+

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Numerical Differential Equation

Numerically solve a differential equation using a variety of classical methods.

Solve an ODE using a specified numerical method:

solve y'(x) = -2 y+x apply heun method

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Specify an adaptive method:

solve {y'(x) = -2 y, y(0)=1} from 0 to 10 using r k f algorithm

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Statistical Inference

Use statistics and hypothesis tests to infer information from a dataset.

Find the sample size needed to estimate a binomial parameter:

sample size for binomial parameter

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Compute a confidence interval for a population mean:

t-interval xbar=4.15, s=0.32, n=100

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Civil Engineering

Calculate the forces on structures, such as bridges and buildings, that we use every day.

Compute the deflection of a beam under load:

beam deformation

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Compute the mandated ventilation rate:

indoor air quality, 3 bedrooms, 1600 sq ft

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Mechanical Enginnering

Look up information regarding mechanical engineering formulas and constants for topics including refrigeration and materials science.

Determine the Poisson ratio value for a deformation:

poisson effect with original length 2m and width 1m

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Analyze a refrigeration cycle:

refrigeration cycle

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Nuclear Physics

Explore aspects of nuclear physics, including radiation and nuclear power.

Compute nuclear weapon effects:

cloud height for a 1 megaton nuclear explosion

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Do carbon-dating computations:

carbon-14 dating, ratio=0.25

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Application of Calculus

Use calculus tools, such as integrals and derivatives, to calculate properties of curves, surfaces, solids and planar regions.

Compute properties of a surface of revolution:

revolve f(x)=sqrt(4-x^2), x = -1 to 1, around the x-axis

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Find inflection points in a specified domain:

inflection points of e^sin(x^3)-1 with -2<=x<=2

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Complex Analysis

Analyze functions and expressions containing imaginary numbers or complex variables.

Compute the residue of a function at a point:

residue of 1/(z^2+4)^2 at z=2i

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Determine the harmonic conjugate:

harmonic conjugate x^3 - 3 x y^2

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Aerospace Engineering

Explore data about aircraft, rockets, satellites or space probes.

Compute airflow around a standard airfoil:

NACA 0012 airfoil

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Do computations with satellite properties:

altitude Navstar 14 / Navstar 32

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Electrical Engineering

Explore the applications of the electromagnetic force for various practical purposes.

Calculate the self-inductance of a coaxial cable:

coaxial cable self-inductance

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Compute characteristics of a transformer:

transformer 110V, 60Hz

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Quantum Physics

Explore quantum phenomena, such as scattering and quantum states.

Get information about quantum phenomena:

Heisenberg uncertainty principle Δx=1nm

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Find equations associated with a quantum system:

quantum particle in a time‐independent 1d potential

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Particle Physics

Get information about particles and their interactions.

Get particle collision data for specified beam types:

pion beam interactions

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Get data about nuclear fission reactions:

uranium 238 half-life

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Continuity

Find discontinuities and continuous intervals of a function. Also determine whether particular discontinuities are removable or infinite due to an asymptote.

Determine continuity at a given point:

is tan(x) continuous at pi?

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Locate discontinuities of a function:

discontinuities (x^3+8)/(x^3+3x^2-4x-12)

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Personal Health

Compute nutritional information about the food you eat or the energy expenditure for your daily activities.

Compute caloric expenditure:

walking 45min, 4mph

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Compare the amount of a particular nutrient in multiple foods: