Here is one option (starting with a fresh connection):
1. create a parameter called "Days Out", that is an integer.
2. create calc field "Amount in Range":
IF [date]-[release date]<=[Days Out] THEN [amount] END
Sum this field, and you will have the sum amount within the "days out" range.
If you want to see this as a running total, then:
1. create a calc field named "Day":
2. another for use as a filter, keeping only when True:
3. place Day as a continuous discrete on the Columns shelf
4. place "amount" on the Rows shelf, and enable the Running Total Quick Table Calculation
this is also in the attached.
Thanks Joe, that works perfectly and even answers my logical follow-up question!
Although I'm not really understanding the rationality behind: IF [date]-[release date]<=[Days Out] THEN [amount] END
How does it know for example, that IF 10<=15 THEN only display the total amount for the first 15 days?
(You don't have to answer that if you don't want to...just trying to wrap my brain around why it works)
The comparison test of [date]-[release date]<=[Days Out] happens at the row level in the data source, in your example of 10<=15, that would result in True, so the IF statement would return the value for [amount] for that record in the data source.
Then the SUM() aggregation in the pill aggregates all those records that passed the test, resulting in the sum of amount for those dates in the desired range.