# How to evaluate the integral and find values

I have following the following integral,

$$\int_{-1}^{1} \sqrt{(1-a+0.5(1+2b))\left(\frac{1}{r^{6}-1+i 0^{+}}- (a+2b)\right)}dr= \Pi$$

I want to draw a plot of how $b$ vary when $a$ varies from $0.5$ to $1$. I can't evaluate this integral symbolically due to the singularity. To remove the singularity I can add a small imaginary part to the integration.

$$\int_{-1}^{1} \sqrt{(1-a+0.5(1+2b))\left(\frac{1}{r^{6}-1+i 0^{+}}- (a+2b)\right)}dr= \Pi$$

But even after that, I have the difficulty of finding a way to numerically solve this equation in Mathematica to find $a$ and $b$ values.

f[b_?NumericQ, a_?NumericQ] := With[{ep = 10^-12(*You may change it*)},