In regards to the attached database/table, the following query returns only 9 rows and skips values for some regions, unlike older versions of MySQL (such as 5.0.95 on CentOS 5 Linux):

SELECT region, NAME, population/area AS dichte FROM cia c WHERE
population/area = (SELECT MAX(population/area) FROM cia cc WHERE
c.region = cc.region);

This appears to be a result of precision issues with floating point values affecting value comparisons.

The following two queries which are equivalent give different result sets:

SELECT region, NAME, population/area FROM cia c WHERE population/area =
(SELECT MAX(population/area) FROM cia cc WHERE area<150000 AND c.region
= cc.region) AND AREA<150000;

SELECT region, NAME, population/area FROM cia c WHERE AREA<150000 AND
population/area = (SELECT MAX(population/area) FROM cia cc WHERE
area<150000 AND c.region = cc.region);