I'm looking for the RegEx syntax for matching all IP addresses that
are NOT in the range of 200.100.100.125  - 200.100.100.175

I'm also looking for the RegEx for matching all IP address that are
not 200.100.100.176

I will test the answers using RegEx Coach.

I have no idea that such a tool (Regex Coach) exists. It is simple,
but works. Thanks! The expressions to match your strings might look a
bit cumbersome (see below), I would avoid using regex for matching
numers.

This one should work with no-range:

((2(([0-4]\d)|5[0-5]))|(1?\d{1,2}))\.((2(([0-4]\d)|5[0-5]))|(1?\d{1,2}))\.((2(([0-4]\d)|5[0-5]))|(1?\d{1,2}))\.((2(([0-4]\d)|5[0-5]))|(1[0189]\d)|(12[0-4])|(17[6-9])|(\d{1,2}))

This one should work with no-particular ip:

((2(([0-4]\d)|5[0-5]))|(1?\d{1,2}))\.((2(([0-4]\d)|5[0-5]))|(1?\d{1,2}))\.((2(([0-4]\d)|5[0-5]))|(1?\d{1,2}))\.((2(([0-4]\d)|5[0-5]))|(1[0-689]\d)|(17[0-57-9])|(\d{1,2}))