This is a function that I use often at the ghci prompt. There are a few ways to write it, none of which I am particularly fond of, but they are all reasonably clean:
fpow n f x = iterate f x !! n
fpow n f = foldr (.) id $ replicate n f
fpow n = foldr (.) id . replicate n -- just eta the above
fpow 0 f = id
fpow n f = f . fpow (n-1) f
The middle two appeal to me because my brain has chunked foldr (.) id to mean "compose a list of functions".
I kinda just wish it were in the prelude :-).
