Thanks, Scott. I don't believe that complexplot3d does the same thing as I need. I believe that it plots |f(z)| over the given 2D domain.
The good news is that I have figured out what was wrong. The option in plotcompare that allows one to plot just the real and imaginary parts of a single function, as opposed to two functions, is expression_plot. The mistake I was making was this: When one is writing a command, one is in MATH input mode. The underscore character is reserved in this mode. It is the shortcut for subscript. Thus, when I typed underscore, I was actually inputting a subscripted hyphen. These look the same to the untrained eye. (I have untrained eyes.) What I now know that I needed to do was use the escape character "\" before the underscore actually input an underscore.
If Maple programmers are scanning these posts, you folks might want to avoid, in future versions, having reserved characters like underscore as part of an argument for a command.
Now, I have a new question: If one only wants the real and imaginary parts of a single function, must one type the same function in twice? It seems that way. The plotcompare command wants its first two arguments to be complex functions. Is there any way around this? (Mind you, this is only an inconvenience, not an impediment.)