differential operator in maxima



Hi All.

I just have swithced from Maple to Maxima. There are some things i can't figure out: i defined a function F(x), and i need to evaluate first derivative of F at x=0. When in Maple, i could do D(F)(0). In Maxima i can DIFF(F(x),x), but not EV(DIFF(F(x),x),x=0). Is there any analog of Maple's D operator? 

Also i wonder how could i define a function which argument and value are at their turn functions, for example the following symmetrizing linear operator:

AF(x) = 1/2(F(x)+F(-x))

In Maple this would be A:=F->unapply(1/2*(F(x)+F(-x)),x); 
then A(exp)(x) = 1/2*(exp(x)+exp(-x)).
In Maxima expression like A(F)(x) leads to error.

Please excuse me if these questions are too stupid.

Regards, tws.