Well,
aidey_f - I refer here, as I do with anything the flight crew can operate, to only those things they have control over. The installed rating of the engine cannot be changed by the flight crew, so only that is considered the maximum power rating, regardless of what the engine is actually capable of.
I thought that comment was unnecessarily confusing to this subject!
mutt - It's quite simple really, the maximum rating of an installed engine is what you get when the TOGA is pushed for a full rated takeoff.
"Up to the maximum t/o power available" seems pretty clear!
The derate is the limiting factor when used, it's considered the maximum for that takeoff, otherwise lowering the Vmcg for the derate, then using full rated power when one fails, will have you red-faced sitting in a ditch somewhere adjacent to the runway perimeter!
Cheers, FD