It looks like you've uploaded a mathematical problem in Persian, involving multiple integrals. Let's break it down and solve the following integrals:

1. $\int_{-3}^{3} \int_{0}^{\frac{\pi}{2}} \left( y + y^2 \cos(x) \right) \, dx \, dy$
2. $\int_{0}^{1} \int_{0}^{1} e^{x+y} \, dx \, dy$
3. $\int_{1}^{2} \int_{x}^{e} e^{\frac{x}{y}} \, dy \, dx$

I will now proceed to solve each integral step-by-step. sympy import symbols, integrate, cos, exp, pi, E

Defining the variables

x, y = symbols('x y')

Solving the first integral

integral1 = integrate(integrate(y + y**2 * cos(x), (x, 0, pi/2)), (y, -3, 3))

Solving the second integral

integral2 = integrate(integrate(exp(x + y), (x, 0, 1)), (y, 0, 1))

Solving the third integral

integral3 = integrate(integrate(exp(x/y), (y, x, E)), (x, 1, 2))

integral1, integral2, integral3Here are the results for the integrals:

1. The result of the first integral is $18$.
2. The result of the second integral is $-e + 1 + e \cdot (-1 + e)$.
3. The third integral has a more complex result involving the Exponential Integral (Ei function):

- \frac{e^2 \cdot e^{e^{-1}}}{2} - \frac{3e}{2} - 2 \cdot Ei(2e^{-1}) - \frac{e \cdot e^{e^{-1}}}{2} + \frac{Ei(e^{-1})}{2} + \frac{3 \cdot Ei(1)}{2} + \frac{e \cdot e^{2e^{-1}}}}{2} + \frac{e^2 \cdot e^{2e^{-1}}}{2}

Would you like further details on any of these integrals or additional clarifications?

Here are some related questions you might explore:

1. How do you apply the Exponential Integral (Ei) function in integrals?
2. What are the properties of definite integrals involving trigonometric functions?
3. How do we simplify double integrals involving exponential functions?
4. How does the change of limits affect the evaluation of integrals?
5. What is the physical interpretation of these integrals in different contexts?

Tip: Always break down complex integrals step by step, especially when combining functions like exponential and trigonometric terms!