Robert D answered most of your questions...
>
> Also, what exactly is a 'symbolic expression with a free variable' ?
Um, mathematically, look at a book on "symbolic logic". Programmatically,
It is a lisp list or s-expression using the symbol 'x'.
>
> How does it differ from the rhs of
>
> f(x):= x^2 + 2*x;
>
> Apparently, maxima treats them differently.
Yes, as Robert points out, the rhs of a function definition is not
simplified or evaluated immediately.
RJF
PS. If you get to the point where you feel comfortable with all this, it
would be good to write it all out for other people, because your questions
are not unique to you. Nor unique to Maxima :)