My daughter gave me an early Christmas gift of a book from my Amazon Wish List. She bought it locally, and this was the only copy the store had available. Notice how badly the cover is curled. The fiber in the paper has been broken, too. So, just putting weight on it and waiting will not help.
Step 1: Idea
I decided to add something to the back side that would pull the cover back into place. I needed a curved form to do it. I do not know what this is called, but my wife puts bread dough for long loaves onto each half when she bakes certain kinds of bread.