We are given that $\rm{A}03_{16}$ is a base 16 number and we need to convert it to base 10.
To convert a base 16 number to base 10, we can use the formula:
$\rm{A}03_{16} = A \times 16^2 + 0 \times 16^1 + 3 \times 16^0$
We are given that the value of $\rm{A}03_{16}$ is 2563, so we can substitute this value into the equation:
$2563 = A \times 16^2 + 0 \times 16^1 + 3 \times 16^0$
Simplifying, we have:
$2563 = A \times 256 + 3$
Now, we can solve for $A$.
Subtracting 3 from both sides of the equation, we get:
$2560 = A \times 256$
Dividing both sides of the equation by 256, we find:
$A = 10$
The value of X is 10.
The answer is: 10
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Convert $\rm{A}03_{16}$ to a base 10 integer, where the 'digits' A through F represent the values X, 11, 12, 13, 14, and 15 in order.
If we know the answer to the above question is 2563, what is the value of unknown variable X?

### Answer:
