Barit1 you are right. I have been flying B757 and it has 3 options for the TO. TO pwr, Derate, and flexible. TO power states for full power. There are two kinds of derated power TO1 and TO2, reducing TO power by a 12% and a 20% respectively. Flexible is used as usual, regarding on the current rwy performance analysis, introducing the max assumed temperature possible in the FMS.
You also have 3 options for the climb. Max climb power, derated climb1 or climb2 that reduces the climb power by a 6 and 12% respectively.
The A340 has only full TO pwr or flex, but for the climb the ultimate fms has derated1 or d2.
I have used other TO options as CLB power under certain conditions on the CRJ200 and water&glycol injection on the Fairchild metroliner.