Find the area bounded by the two Cartesian equations above. If this area can be expressed in the form with , , , and composite numbers, write your answer as .
Bonus: Using this sum, generalize the bounded area with respect to :
This problem was created in celebration of Pokémon's 20th anniversary.
The picture of the graph was produced from Desmos.
Image Credit: Pokeball by phantompanther, DeviantArt.