Find the area between $f(x)=x^{2}-25$ and the $x$-axis from $x=0$ to $x=10$.

The area is $\square$ square units. (Round answer to two decimal places.)

Step 1 ：The area between a function and the x-axis from a to b is given by the definite integral of the function from a to b. In this case, we need to find the definite integral of the function \(f(x)=x^{2}-25\) from \(x=0\) to \(x=10\).

Step 2 ：However, since the function \(f(x)=x^{2}-25\) is negative for \(x\) values between 0 and 5, we need to take the absolute value of the function to calculate the area.

Step 3 ：So, we need to calculate the definite integral of the absolute value of \(f(x)=x^{2}-25\) from \(x=0\) to \(x=10\).

Step 4 ：We can split this into two integrals: one from 0 to 5 (where the function is negative) and one from 5 to 10 (where the function is positive).

Step 5 ：So, the area is given by: \(\int_{0}^{5} -(x^{2}-25) dx + \int_{5}^{10} (x^{2}-25) dx\)

Step 6 ：Calculating the above integrals, we get \(250/3\) for the first integral and \(500/3\) for the second integral.

Step 7 ：Adding these two areas together, we get a total area of 250 square units.

Step 8 ：Final Answer: The area is \(\boxed{250}\) square units.