You are forgetting the fact that Trinity force applies to your base damage not bonus damage you base is only 120 therefore trinity does 180 more damage that is weak and with 210 ad you would count blood thirster maximum stacks therefore we have to count gun blade stacks and I conquer that AP does more damage. Q = Base Damage 120 (+80) + 250 (lichbane) + (.6AP; 140) + 100 + 200 - 300 = 900

Actually i think the lich bane is wrong...
you have 200ap -> 200 extra damage from lichbane proc
you have 210ad -> 315 extra damage from trinity force

yes i know, lich bane is cheaper but trinity force is just better over all, in my opinion..