Metatrader Trading Question

Imagine the following:

I set a buy stop order EUR/USD at 1.58 for a 10 pip profit, so TP at 1.5810.
I turn my computer off and go to sleep.

Next day I wake up and see that the target has been hit about an hour ago and the TP has been reached.

Will this actually execute at the brokers office, or is this now a non-valid trade as at the time I turned on my computer, the prices were not available?

Question is, are the trades you set desktop based or on a server at the broker?

Trades, SL and TP are stored on the broker's server. Trailing stops are on your platform. Your platform must be running and connected to the internet for Trailing stops and Expert advisers to work.

Great, thanks.

I knew about the EA but not about the trailing stops.
I have a very simple trading method, well one of them anyway. I set a buy stop at the previous day high and a sell stop at the prev day low.
I don't want to be watching and keep the cpu off if possible.
It worked demo but wasn't sure about live.
Thanks again!