I sometimes find myself saying "I need a function that goes through points [0,0] and [1,1] and kind of gradually slopes up." To me, this naturally suggests drawing, not symbolically entering an equation. Even animation programs that let you graphically manipulate animation curves don't let you draw (or perform!) what you want the animation to do.
It would also be fun to manipulate a physical object, like a string or bendy ruler to get the curve you want.
I made a quick prototype that just spits out a polynomial of the equation you drew.
It would also be fun to manipulate a physical object, like a string or bendy ruler to get the curve you want.