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

The area is $◻$ 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 $\boxed{{\displaystyle 250}}$ square units.