How do I work out a rug curl?
Synthetics tend to soften nicely with a little heat. If you're in a warm climate, lay them face down on a clean surface in the sun for a while. They should become noticeably more limp. Bring them inside while still warm and lay them out. 

If you don't have warm sunshine, a heat lamp or other mild heat source could do. Be careful not to melt anything. 

Natural fibers tend to relax with moisture. A clothing steamer or simple spray bottom might be enough.