between

What is wrong with "between"?

You can just combine two filters. One with a ">" and another with a "<" operator.

didn't get how to write that .. how can i send the two values to filter 

i understood your query 

select * from xyz where id> 1 and id<30 like this but how to write in appian!

Use a logical expression

docs.appian.com/.../fnc_system_a_querylogicalexpression.html

t function a!queryFilter [line 62]: Cannot apply operator [GREATER_THAN] to field [expiredDays_int] when comparing to value [TypedValue[it=101,v={1}]].

a!queryEntity(
  entity: cons!CR_CMU_ENTITY_DU_MONITORING,
  query: a!query(
    logicalExpression: a!queryLogicalExpression(
      operator: "AND",
      filters: {
        a!queryFilter(
          field: "expiredDays_int",
          operator: ">",
          value: {
            rule!CR_CMU_DSC_getExpiredDaysInSecurityDocumentation(
              selectedItemType_txt: 1
            ).startIndex_int
          }
        ),
        a!queryFilter(
          field: "expiredDays_int",
          operator: "<",
          value: {
            rule!CR_CMU_DSC_getExpiredDaysInSecurityDocumentation(
              selectedItemType_txt: 30
            ).endIndex_int
          }
        )
      },
      ignoreFiltersWithEmptyValues: true
    ),
    pagingInfo: ri!pagingInfo
  ),
  fetchTotalCount: true()
)

Seems like the value is a list. This must be a single value.

Try the below snippet:

a!queryEntity(
entity: cons!CR_CMU_ENTITY_DU_MONITORING,
query: a!query(
logicalExpression: a!queryLogicalExpression(
operator: "AND",
filters: {
a!queryFilter(
field: "expiredDays_int",
operator: ">",
value: cast(
typeof(tointeger(null)),
rule!CR_CMU_DSC_getExpiredDaysInSecurityDocumentation(selectedItemType_txt: 1).startIndex_int
)
),
a!queryFilter(
field: "expiredDays_int",
operator: "<",
value: cast(
typeof(tointeger(null)),
rule!CR_CMU_DSC_getExpiredDaysInSecurityDocumentation(selectedItemType_txt: 30).endIndex_int
)
)
},
ignoreFiltersWithEmptyValues: true
),
pagingInfo: ri!pagingInfo
),
fetchTotalCount: true()
)

A couple of things to note here:

1. Curly braces in below statement indicates it's an array.

value: {
rule!CR_CMU_DSC_getExpiredDaysInSecurityDocumentation(
selectedItemType_txt: 30
).endIndex_int
}

It's like writing your SQL as below which obviously results in an error (Appian presents it similar to what you have in your question): 

select * from xyz where id > {1}

2. I have used the cast function to ensure your rule returns a scalar value but not a list. If your rule is returning a scalar value, then you can write as below too:

a!queryFilter(
field: "expiredDays_int",
operator: "<",
value: rule!CR_CMU_DSC_getExpiredDaysInSecurityDocumentation(selectedItemType_txt: 30).endIndex_int
)