Hello, elizsimca!
Set up the integral to find the area shared by the polar curves given by:
. .
I found the points of intersection: . . . . . Good! The first curve is a 4leaf rose curve.
The petals at one unit long and are aligned along the ±45° lines.
The second is a circle centered at the origin with radius ½.
We are in Quadrant 1.
We want the area of that petal which is inside the circle. Code:

 *
 * /
* * /
 .* / *
 .:::::*
*::::/::* *
:::/:::::*
:/:::* *
 *     *    

I'm afraid it takes three integrals . . .