Lol come on man.

Don't try to gocha me with your leading questions, "man"!

said capitalism is the economic system of a state. You started going on about international trade, making it sound like "nations compete therefore capitalism is all trade".

Your conclusion is false. It's actually: Capitalism requires nations to compete.

I tried to help you understand by proposing the question of whether a communist state can trade with a capitalist state

If a "communist" state (which is an oxymoron, since communism is by definition stateless) trades with a capitalist state, it's in a capitalist context. The states interact on a capitalist world market.

So that you understand that capitalism is not defined by international trade.

International trade is a consequence of capitalism in a world of nation states.