Is it possible to get a function (polyfit etc.) based on several equations like x coordinate of maximum, integral, a few points

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Dear all,
I have a problem that I need to get a procedure which generates a cubic polynom with the following data given:
0:1:100
1) Point at (5,0)
2) y(x=100)<=6
3) Integral graph =1
4) Maximum at x_max
So the function principally has a optional look, but it needs to meet the 4 equations. Does anyone know a way which helps to solve?
Best and thank you in advance, Jan

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