> f:=2-x;           One way is by assigning a formula to a name.
 > plot(f,x=-1..1);  If you use this method you can refer to f,
 > solve(f=0,x);     BUT referring to "f(x)" yields nonsense.
 > f(x);      WRONG      
                                     2 - x(x)
 
 
 > f:=x->x^2;          Another way is by using an arrow. 
 > f(x);               If you use this method you can refer to f(x),
 > f(1);               BUT referring to just "f" only yields "f",
 > plot(f(x),x=-1..1); not the function.
 > solve(f(x)=0,x);
 > f;         WRONG
                                       f

 
 > f(x):=2-x;        This assigns the formula to the name "f(x)",
                     but for f(1) and similar expressions Maple
                     just returns the same thing you type in.

 
 > f=2-x;            This is an assertion rather than an assignment,
                     so it doesn't change the value of f at all,
                     and for f Maple will just return the name "f"
                     rather than 2-x.