Maxima has many standard simplifications which it performs on every
expression. Maxima is not designed to preserve unsimplified
expressions such as x+0 (simplifies => x), x+x (=> 2*x), x/x (=> 1),
(a/2)^2 (=> a^2/4), etc.
There are two main ways of blocking these default simplifications. One
is to turn off simplification entirely, by setting simp:false. This
will then give you results like integrate(x,x) => x*x*2^-1 and
diff(integrate(x,x),x) => 0*x*x + 1*x*2^-1 + 1*x*2^-1. And some
built-in functions will not operate correctly on unsimplified
expressions.
Another is to "box" subexpressions. Thus, box(a/2)^2 does not
simplify, but the boxed part gets treated as a, um, black box e.g.
diff(box(x),x) => 'diff('box(x),x). Judicious use of boxing and
unboxing may have the effect you want. Or maybe not, depending on what
you're trying to accomplish.
-s