Weekly Challenge 43: A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

Weekly Challenge 28: the Right Volume

Can you rotate a curve to make a volume of 1?

Weekly Challenge 24: Suspicious Integrator

Stage: 5 Challenge Level:

I asked my integrating application to work out this integral:

Integrate[1000000/(10 + (1000000 - 10)/2^(4*x)), x]

Try to evaluate this expression at $x=1$. What has gone wrong? Can you work out the actual real answer and verify by differentiation?