Find the area of the shaded region. \[ f(x)=10 x+3 x^{2}-x^{3}, g(x)=0 \]

Step 1 ：The area of the shaded region between two functions, f(x) and g(x), from a to b is given by the integral from a to b of the absolute difference between the two functions. In this case, g(x) is 0, so we just need to find the integral of the absolute value of f(x) from a to b.

Step 2 ：However, we don't have the limits of integration (a and b) given in the question. We need these limits to calculate the area. Without these limits, we can't proceed with the calculation.

Step 3 ：If we assume that the shaded region is between the x-intercepts of the function f(x), then we need to find the roots of the equation f(x) = 0. These roots will be our limits of integration.

Step 4 ：The roots of the equation are -2, 0, and 5.

Step 5 ：By integrating the function f(x) from -2 to 5, we find that the area of the shaded region is \(\frac{407}{4}\).

Step 6 ：Final Answer: The area of the shaded region is \(\boxed{\frac{407}{4}}\).