#bash - 32 31 17 14 characters + length of X, Y and Z
Thanks to devnull for suggesting seq!
seq [X] [Y]|grep -c [Z] e.g. X = 100, Y = 200, Z = 20
$ seq 100 200|grep -c 20 2 e.g. X = 100, Y = 200, Z = 10
$ seq 100 200|grep -c 10 11 e.g. X = 0, Y = 1000000, Z = 2
$ seq 0 1000000|grep -c 2 468559