Maple is a symbol manipulator.

Exact arithmetic:

>	1/29+1/31;

>	arcsin(1/2);

>	exp(I*Pi);

Can give numerical answers to arbitrary precision:

>	evalf( arcsin(1/2), 10);

>	evalf( arcsin(1/2), 40);

>	evalf( Pi, 1000);

Note default of evalf is 10 digits:

>	evalf(Pi);

Algebraic expressions:

>	restart;                 Also discuss saving work

>	a:=x^2*exp(x)*cos(x);

>	diff(a,x);

>

int(a,x);

>	I:=int(a,x=-Pi..Pi);

Error, illegal use of an object as a name

>	I1:=int(a,x=-Pi..Pi);

>	simplify(I1);

>	factor(I1);

>	plot(a,x=0..Pi/2);

Note last thing is NOT a symbolic procedure!

Using Maple to solve equations:

>

restart;

>	a:= x^2-3*x+1=0 ;

>	solve(a,x);

>	solve( {x+s*y=t,2*x-y=s*t} , {x,y} );

>	solve( {x+s*y=t,2*x-y=s*t} , {t,y} );

>	a:= x=(1+x^2)*cos(x) ;

>	solve(a,x);

>	fsolve(a,x);

This is numeric....but matlab does not really have it

>	plot( (1+x^2)*cos(x)-x  , x = -3..3);

>	fsolve(a,x=-3..-1);

Some linear algebra

>

restart;

>	with(LinearAlgebra);

>	M1:=<<1,t,-3>|<3,1,t+4>|<4,6,1>>;

>	Determinant(M1);

>	solve(Determinant(M1)=0,t);

>	M2:=<<1,-5,-3>|<3,1,-1>|<4,6,1>>;

>	Determinant(M2);

>	ColumnSpace(M2);

>	Eigenvalues(M2);

>	Eigenvectors(M2);

>	Eigenvalues(M1);    this is going to involve solving a cubic....maple is bad at this.

There is now  a package to do strictly numerical  linear algebra on maple....but I use matlab

Programming in maple:

>	x:=1/2;  for i from 1 to 10 do x:=5/2*x*(1-x) end do;

>	x:=1/2;  for i from 1 to 20 do x:=evalf(5/2*x*(1-x)) end do;

This of course would better be done in matlab

More generally can write functions known as procedures

Graphics

>

restart;

>	with(plots);

Warning, the name changecoords has been redefined

Note: plotting is de facto numeric...better done in matlab but maple has nice procedures (and I know it)

>	animate( sin(x*t), x=-10..10, t=0.5..1);

>	implicitplot3d( x^2-x+2*y+3*z=1, x=-5..5, y=-5..5, z=-10..5, axes=boxed, style=patchnogrid);

>

>	animate3d(cos(t*x)*sin(t*y),x=-Pi..Pi, y=-Pi..Pi,t=1..2);

>