I’m really posting this for myself to act as a big paperweight. Whenever I forget about := and : for functions in Maxima, I can refer to this page.
The gist:
- g(x):=x^2 results in a function you can evaluate as g(3)
- f: x^2 results in an expression you can evaluate with ev(f,x=3)
- ev works with both: ev(g(x),x=3) or ev(f,x=3)
- also subst(x=3,f) and subst(x=3,g(x))
- based on our definition, g doesn’t have a meaning…only g(x) does
- likewise, f(3) doesn’t have a meaning here…only the symbol f does
- finally h:=x^2 gives an error — explicit dependent variable needed with :=
The MaximaList 
This is a great “paperweight” post! I’d add one thing I just had to look up that seems to fall into this category on turning an expression into a function: https://stackoverflow.com/questions/67442195/convert-an-expression-to-a-function
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