For comparison, I translated it pretty directly to Python:

    import sys
    from math import sqrt
    
    def string_palindrome(num):
        s = str(num)
        return s == s[::-1]
    
    sys.stdin.readline() # throw away first line (number of cases)
    
    for count, line in enumerate(sys.stdin):
        found = 0
        start, finish = [int(num) for num in line.split(" ")]
        sqrt_start  = int(sqrt(start ))
        sqrt_finish = int(sqrt(finish))
    
        for x in xrange(sqrt_start, sqrt_finish+1):
            if string_palindrome(x):
                square = x * x
                if string_palindrome(square) and start <= square <= finish:
                    found += 1
    
        print("Case #%d: %d" % (count, found))

For the first 15 test cases I get the following run times:

    pypy 2.0-beta2: 1.6 seconds
    pypy 1.9:       2.1 seconds
    ruby 1.9.3p194: 3.7 seconds
    python 3.3.0:   5.9 seconds
    python 2.7.1:   6.2 seconds

The integer version for checking palindromes was also much slower in python.

Edit: Even though the interger version of _palindrome is slower in pypy, there's another optimization that works there, but is slow in cpython. It brings the run time down to 0.6 seconds!

    def half_string_palindrome(num):
        num_str = str(num)
        num_len = len(num_str)
    
        for i in xrange(0, num_len // 2):
            if num_str[i] != num_str[num_len - i - 1]:
                return False
    
        return True