3. Calculate the area of the set of points on the coordinate plane that satisfy the inequality $(y+\sqrt{x})\left(y-x^{2}\right) \sqrt{1-x} \leqslant 0$.
Solution. The left side makes sense only for $0 \leqslant x \leqslant 1$. In this case, it is required that $y+\sqrt{x}$ and $y-x^{2}$ have different signs (or one of them equals zero), or that $x$ equals 1. If we exclude the case $x=1$ (which gives a zero area), we are left with a part of the plane bounded by the segment of the line $x=1$ and parts of the parabolas $y=-\sqrt{x}$ and $y=x^{2}$. By cutting this figure into two parts along the x-axis and placing the upper part below the lower one, we get a square of area 1.

Answer: the area is 1.