How to distribute data over a certain period in Google Spreadsheets (dynamically when adding, changing)?

Question

Google Sheets

https://docs.google.com/spreadsheets/d/1w8GSKNTem7...
in sheet 9 of the document there is a table with a range of dates and a value for these dates, sheet 8 - the distribution of values ​​for each date of the full range (1 year).
As it should be (column "Answer"):
from 01/01/2021 to 03/04/2021 - value 67
from 03/04/2021 to 09/09/2021 - value 78 ... etc. until the end of the fixed list (1 year - by day )
There is a solution (sheet 8, columns "" Sample, " Sample 2"), which works if the number of ranges on sheet 9 is static (5 ranges are specified), if you set 6, 7 ...., then it is necessary to change the formula, with a decrease too.
We need a solution in which adding or decreasing the number of ranges (rows with ranges),
Thanks in advance to everyone for ideas.

Answer 1

=VLOOKUP(A2;SORT('лист9'!A$1:B$15;1;1);2;1)
The sorting function is needed to exclude the case of incorrect arrangement of dates in the range from which the values ​​will be taken.

PS

Никогда, кажется, не использовал ВПР для поиска ближайших значений, только для точного соответствия. Было интересно. Спасибо за вопрос.