I want to create a custom page for my WordPress blog that will execute my PHP code in it, whilst remaining a part of the overall site CSS/theme/design.

The PHP code will make use of third-party APIs (so I need to include other PHP files).

How do I accomplish this?

N.B.: I do not have a specific need to interact with the WordPress API - apart from including certain other PHP libraries, I need I have no other dependencies in the PHP code I want to include in a WordPress page. So obviously any solution that didn't require learning the WordPress API would be the best one.