### How to use sage to solve this problem?

Suppose we have an equation:
$${(y\cos{(x)}+u})^{2}+{(-(y\sin{(x)}+v)^3+1)}^{\frac{2}{3}}=1$$

The graph of this implicit relation has two regions, where one part is above the x-axis, and the other part is below the x-axis.

Suppose we're are trying to find the area of the relation above the x-axis, from the domain ${0}\le{x}\le{2\pi}$. How can one solve for the values of u and v that can give the highest area for this equation that's is above the x-axis.

Here is a brief illustration:

~~Copy and paste the link into the internet:~~

~~(C:\Users\Bharathmon\Pictures\Average Radius\AverageRadiusProblem.PNG)~~

If you find the picture try Note: The blue stripes should stop at $2\pi$, and ~~use sage to graph ~~if the equation ~~above, with respect ~~has regions that "UNDEFINED", try to ~~u and v.~~ignore it.