# 2015 Countdown Problem #15: Palindrome Integration

**Algebra**Level 5

the next palindrome larger than \(x\) (if \(x\) is not a palindrome); or

\(x\) (if \(x\) is a palindrome).

For example, \(f(1001)=1001\),\(f(1001.01)=f(1002)=1111\).

Let

\[A=\int _{ 999 }^{ 2015 }{ f(x) \mbox{ } dx } \]

\[B=f(...(f(f(1603)-58)-58)...)-58\]

Find the value of \(\frac{A}{B}\).

*This problem is part of the set 2015 Countdown Problems.*