Find the area enclosed by circle `x^(2)+y^(2)=4`, parabola `y=x^(2)+x+1`, the curve `y=[sin^(2)x/4+cos x/4]` and X-axis (where,[.] is the greatest integer function.

If the area bounded by circle x ^(2) + y^(2)=4, the parabola y = x ^(2) + x+1 and the curve y = [sin ^(2) ""(x)/(4) +cos ""(x)/(4)], (where [] denotes the greats integer function) and x-axis is (sqrt3 + (2pi)/(3) - (1)/(k)), then the numerical quantitity is should be :

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