SELECT User_ID from Database
ORDER BY RAND()
LIMIT 10
group by User_ID

select d.*
from (select d.*,
             (@rn := if(@u = user_id, @rn + 1,
                        if(@u := user_id, 1, 1)
                       )
             ) as rn
      from (select d.* from database d order by user_id, rand()
           ) d cross join
           (select @u := 0, @rn := 0) params
     ) d
where rn <= 10;