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

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

[Walter Roberson]

Does n3 mean cubic in this context?

[Jan GimpelHenning]

Yes, sorry for misunderstanding