(*^
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Algebra and Calculus
:[font = text; inactive; preserveAspect]
Algebraic formulas:
:[font = input; preserveAspect]
9(2+x)(x+y) + (x+y) ^2
:[font = text; inactive; preserveAspect]
Algebraic manipulations, e.g. Expand the 3rd power of the above polynomial:
:[font = input; preserveAspect]
Expand[%^3]
:[font = text; inactive; preserveAspect]

Factorization, e.g. factor the above polynomial over the integers:
:[font = input; preserveAspect]
Factor[%]
:[font = text; inactive; preserveAspect]

Integration, e.g. analytically calculate the indefinite integral Ú dx x2 sin(x)2:
;[s]
7:0,0;66,1;67,0;72,2;73,0;80,2;81,0;83,-1;
3:4,13,9,Times,0,12,0,0,0;1,18,13,Symbol,0,12,0,0,0;2,21,13,Times,32,12,0,0,0;
:[font = input; preserveAspect]
Integrate[x^2 Sin[x]^2, x]
:[font = text; inactive; preserveAspect]
Differentiation, e.g. differentiate the above result with respect to x:
:[font = input; preserveAspect]
D[%,x]
:[font = text; inactive; preserveAspect]
Simplification, e.g. simplify the resulting expression:
:[font = input; preserveAspect]
Simplify[%]
:[font = text; inactive; preserveAspect]
Series Expansions, e.g. generates a power series expansion for x2 sin(x)2 about the point x = 0 to order 14:
;[s]
5:0,0;64,1;65,0;72,1;73,0;109,-1;
2:3,13,9,Times,0,12,0,0,0;2,21,13,Times,32,12,0,0,0;
:[font = input; preserveAspect]
Series[%, {x,0,14}]
:[font = text; inactive; preserveAspect]

Check the error order of the central difference differentiation formula by power series expansion around h=0 to 6th order:
:[font = input; preserveAspect; endGroup]
Series[(f[x+h] - f[x-h])/(2h), {h,0,6}]
^*)