E Power Eye Pie Plus One

Calculus Level 3

If the following integral equals to ZZ

0π/2((sinx)cosx(cosx)sinx)dx \large \displaystyle \int_0^{\pi /2} \left ( (\sin x)^{\cos x} - (\cos x)^{\sin x} \right) \mathrm{d}x

What is the value of 1000Z\lfloor 1000Z \rfloor ?

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