That looks a lot like an EGR pipe.

Can you post a picture of your broken one in action?

Also can you post a picture of the actual break?

not until I pull it out

Cathedral Club that looks like the pipe that comes off the bottom of the air pump solenoid and attaches to each runner of the exhaust manifold....

Weird, I can't find it anywhere either.

Either way, that shouldn't cause the car to have power issues . . . unless it was completely missing causing crazy oxygen sensor readings. But even that would be a stretch.