The value of $$\frac{8}{\pi}\int_0^{\pi/2} \frac{\cos x^{2023}}{\sin x^{2023} + \cos x^{2023}} dx$$ is ______.

We need to evaluate $$\frac{8}{\pi}\int_0^{\pi/2} \frac{(\cos x)^{2023}}{(\sin x)^{2023} + (\cos x)^{2023}} dx$$.

A well-known property states that for any function $$f$$, $$\int_0^{\pi/2} \frac{f(\cos x)}{f(\sin x) + f(\cos x)} dx = \frac{\pi}{4}$$.

If we set $$I = \int_0^{\pi/2} \frac{(\cos x)^{2023}}{(\sin x)^{2023} + (\cos x)^{2023}} dx$$ and substitute $$x \to \frac{\pi}{2} - x$$, we obtain $$I = \int_0^{\pi/2} \frac{(\sin x)^{2023}}{(\cos x)^{2023} + (\sin x)^{2023}} dx$$.

Adding these two expressions gives $$2I = \int_0^{\pi/2} 1 \, dx = \frac{\pi}{2}$$, so that $$I = \frac{\pi}{4}$$.

Therefore, $$\frac{8}{\pi} \times \frac{\pi}{4} = 2$$.

The answer is 2.