you may b right, but i have never read that fasting in ramadan gives reward of 30 x 10 = 300 days (if someone doesnt fast in shawwal)
if i'm not wrong, one gets rewarded for the whole year because good deeds are multiplied by 10, hence: 30 days of ramadan x 10 = 300 days 6 days of shawwal x 10 = 60 days the reward is equal to 360 days of fasting. --- one does not have to begin these six days on the second day of shawwal nor do they have to be six consecutive days.
The Prophet Muhammad (صلى الله عليه وسلم) is reported to have said, "Whoever fasts the month of Ramadhan and then follows it by fasting six days during the month of Shawwaal will be rewarded as if he had fasted the entire year." [Related by Muslim, at-Tirmithi, Ibn Majah, Abu Dawood and Ahmad by way of Jabir]. jazakAllah