Consider the surfaces 
and 
- in `z' form.
We plot them using
plot3d ( {x^2 + y^2, 6 - x^2 - y^2} , x=-2..2 , y=-2..2 ) ;
Be patient - you should see two paraboloids.
The colors on the monitor may behave strangely - activating
the picture window will correct the problem. (Be sure your NumLock
light is off.)
From the Style menu choose Patch and Contour and from the
Axes menu choose Boxed. Now move arrow to black part and type
p to plot the picture again. Note the boxed picture and the axes.
To obtain a better view of the picture rotate the box - a reasonable view
is obtained when 
- and type p again.
To improve the picture, from Color choose Lighting Scheme 3.
Try the other menus and observe their impact on the picture.
To get rid of the picture type q (for quit) in the picture window.
Drawing one or more surfaces in `z' form is completely analogous. However one difficult part of plotting surfaces is choosing the appropriate range for x and y - some theoretical analysis and trying various choices usually results in the best picture.
Surfaces given implicitly such as the ellipsoid 
are plotted using the implicitplot3d command in the plots package
with(plots); only once in a Maple session implicitplot3d( (x^2)/4 + (y^2)/9 + (z^2)/8 = 1, x=-2..2, y=-3..3, z=-3..3 );From the Projection menu choose the Constrained option to obtain the true shape. Notice we had to enter ranges for x,y and also z, unlike for
plot3d. Further, the range is important - only the part
of the surface inside the range box will be displayed. So a blank picture
will be displayed if the surface is outside the range box.
In some cases, the picture may not be very smooth - this can be improved by
increasing the grid (use ?implicitplot3d to find more about it).
Surfaces which can be drawn using plot3d can also be drawn using
implicitplot3d but the latter is slower so use plot3d wherever
possible.