For one, [man]file_get_contents/man is just going to give you the raw PHP code from the filesystem. If you actually want the PHP code in that file to be parsed and executed, then you'd want to [man]include/man or [man]require/man it instead.
Even then, you're not invoking it the same way you would if you opened a web browser and requested that same file - instead you're directly loading that script off the local file system and executing it as PHP code. Thus if it's looking at $COOKIE or $POST, then you could simply populate those arrays with the data it expects before you include/require it.
If you're actually talking about some remote webpage, then you'd want to use [man]cURL[/man] to send a POST request to it, along with whatever form data and/or cookie(s) are appropriate.