[b]Evaluate[/b] $\int^{\pi/2}_0 \frac{\cos^4x + \sin x \cos^3 x + \sin^2x\cos^2x + \sin^3x\cos x}{\sin^4x + \cos^4x + 2\ sinx\cos^3x + 2\sin^2x\cos^2x + 2\sin^3x\cos x} dx$

A substitute teacher lead a groop of students to go for a trip. The teacher who in charge of the groop of the students told the substitude teacher that there are two students who always lie, and the others always tell the truth. But the substitude teacher don't know who are the two students always lie. They get lost in a forest. Finally the are in a crossroad which has four roads. The substitute teacher knows that their camp is on one road, and the distence is $20$ minutes' walk. The students have to go to the camp before it gets dark. $(1)$ If there are $8$ students, and $60$ minutes before it gets dark, give a plan that all students can get back to the camp. $(2)$ If there are $4$ students, and $100$ minutes before it gets dark, is there a plan that all students can get back to the camp?