Average Running total each quarter interval

Try this:

Qtr Avg Running Total 3 = 
// Get latest visible date with data
VAR LatestDateWithData =
    CALCULATE (
        LASTNONBLANK ( Dates[Date], [Total Revenue] ),
        ALLSELECTED ( Dates )
    ) // Get earliest YearQuarter
VAR EarliestQtr =
    CALCULATE ( MIN ( Dates[YearQuarter] ), ALL ( Dates ) )
VAR LatestMonthNumber =
    MONTH ( LatestDateWithData ) // Get month number of latest date
VAR QuarterNumber4Start =
    EDATE (
        CALCULATE ( MINX ( STARTOFQUARTER ( Dates[Date] ), [Date] ), ALL ( Dates ) ),
        3 * 3
    )
VAR LatestYearQuarter =
    FORMAT ( LatestDateWithData, "YYYY0Q" ) // Get YearQuarter key of latest date
VAR RowQuarter =
    MAX ( Dates[YearQuarter] ) // Get YearQuarter key for current row
VAR QuarterEnds = { 3, 6, 9, 12 } // Quarter end months
VAR StartOfQtr =
    MINX ( STARTOFQUARTER ( Dates[Date] ), [Date] )
VAR StartOfPrevQtr = StartOfQtr - 1 // Day before start of current quarter
VAR _Result =
    IF (
        HASONEVALUE ( Dates[YearQuarter] ),
        SWITCH (
            TRUE (),
            StartOfQtr <= QuarterNumber4Start, 0, // Show 0 if earliest quarter
            LatestYearQuarter = RowQuarter
                && NOT LatestMonthNumber
                    IN QuarterEnds && ISFILTERED ( Dates[YearQuarter] ), 0, // Show 0 if latest incomplete quarter
            CALCULATE (
                AVERAGEX (
                    VALUES ( Dates[YearQuarter] ),
                    [Total Revenue]
                ),
                DATESINPERIOD ( Dates[Date], StartOfPrevQtr, -4, QUARTER ),
                REMOVEFILTERS ( Dates )
            )
        )
    )
RETURN
    _Result