what is the difference between "let rec" and just "let"? what does rec
stand for?

are the following defintions exactly the same? at least they seem to
give the same results...

# let rec cube x = x*x*x;;
val cube : int -> int = <fun>
# cube 12;;
- : int = 1728

# let cubex x = x*x*x;;
val cubex : int -> int = <fun>
# cubex 12;;
- : int = 1728
#