Given : \[\displaystyle \int_{0}^{2.\pi} \dfrac{dx}{31+6cosx+5sinx}=\dfrac{\pi}{a}\] Find the value of \[\large \lceil \frac{a^2}{2} \rceil\] It is not exactly the same problem as this one

**Note:**

\(\lceil \lambda \rceil\) denotes ceiling function ( or lowest integer greater than equal to \(\lambda\))

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