If&nbsp;<span class="math-tex">\(f(x)=\sin^5 x + \sin^3 x\)</span>&nbsp;and&nbsp;<span class="math-tex">\(g(x)=\cos^6 x + \sin^3 x\)</span>, then the value of&nbsp;<span class="math-tex">\(\displaystyle\int_0^{\pi/2} [f(x) + f(-x)] [g(x) + g(-x)]dx\)</span>&nbsp;is