Example Maple Code:
Note: Maple doesn't know what e is, unless you define it. The function e^x is typed as exp(x).
So you could type e:=exp(1): and then use e^x after that, or just use exp(x) all the time.

Plotting a surface from its equation:
  with(plots):
  implicitplot3d(x=y^2+z^2,x=0..2,y=-2..2,z=-2..2);

Many options can be used inside the implicitplot3d command to tweek your graph.
Help url: http://www.maplesoft.com/support/help/Maple/view.aspx?path=plots/implicitplot3d

Plotting a space curve with Maple:
  with(plots):
  spacecurve([t,sin(t),cos(t)],t=0..4*Pi,axes=normal,orientation=[15,75],scaling=constrained);

Help url: http://www.maplesoft.com/support/help/Maple/view.aspx?path=plots/spacecurve

Plotting f(x,y) with Maple:
  plot3d(1-x^2,x=-1..1,y=0..1,axes=framed);
  Use the view option to constrain the output (z) range:
  plot3d(1-x^2,x=-1..1,y=0..1,view=0..2,axes=framed);
  Use the orientation option to change the viewpoint:
  plot3d(1-x^2,x=-1..1,y=0..1,view=0..2,orientation=[60,30],axes=framed);
 
(roughly speaking, viewpoint is 60 degrees right of positive x-axis, 30 up from xy plane)
Help url: http://www.maplesoft.com/support/help/Maple/view.aspx?path=plot3d

Plotting contours with Maple:
  with(plots):
  contourplot(x^2+y^2,x=-2..2,y=-2..2,contours=[0,1,2,3,4],scaling=constrained);

Help url: http://www.maplesoft.com/support/help/Maple/view.aspx?path=plots/contourplot

Plotting a surface and contours, and displaying them together:
  with(plots):
  a:=plot3d(x^2+y^2,x=-2..2,y=-2..2,style=patchnogrid,shading=z):
  b:=contourplot3d(x^2+y^2,x=-2..2,y=-2..2,contours=[0,1,2,3,4],color=black):
  display(a,b,orientation=[30,30,0],axes=framed,view=0..4);


Integrating a function with Maple:
   f:=x->x*sin(x);
   int(f(x),x);
   int(f(x),x=1..3);


Doing a double integral (integrating x sin(x+y) over [1,3]x[0,2]):
   f:=(x,y)->x*sin(x+y);
   int(int(f(x,y),x=1..3),y=0..2);


Plotting a spherical function, rho = f(theta, phi):  rho is called r, theta is called t, phi is called p
   r:=(t,p)->1+0.2*cos(6*t);
   plot3d(r(t,p),t=0..2*Pi,p=0..Pi,coords=spherical,scaling=constrained,numpoints=5000,orientation=[30,30,0]);


Plotting a field and a curve together: (this is 13.2 #21)
  with(plots):
  a:=fieldplot([x-y,x*y],x=-2.2..2.2,y=-2.2..2.2,scaling=constrained,arrows=thin,color=red,grid=[23,23],fieldstrength=log):
  b:=plot([2*cos(t),2*sin(t),t=0..3*Pi/2],x=-2.2..2.2,y=-2.2..2.2,scaling=constrained,axes=none,color=black):
  display(a,b,axes=none);