MikroTik RouterOS scripting: passing parameters a dollar at the end of the string requires parenthesis around the string. No need when initialising variables.

showValuesFromDirectInitilisation.output.txt

-----------------------------start
value='^scripts.Function..*'
value='^scripts.Function..*$'
value='^scripts.Function..*$'
value='$'
value='$'
-----------------------------finish

showValuesFromDirectInitilisation.rsc

{
  :local showValuesFromDirectInitilisation do={
    :local value1 "^scripts.Function..*"
    :local logLine1 "value='$value1'"
    :put $logLine1

    :local value2 "^scripts.Function..*\$"
    :local logLine2 "value='$value2'"
    :put $logLine2

    :local value3 ("^scripts.Function..*\$")
    :local logLine3 "value='$value3'"
    :put $logLine3

    :local value4 "\$"
    :local logLine4 "value='$value4'"
    :put $logLine4

    :local value5 ("\$")
    :local logLine5 "value='$value5'"
    :put $logLine5
  }
  :put "-----------------------------start"
  $showValuesFromDirectInitilisation
  :put "-----------------------------finish"
}

showValuesFromParameters.fails.rsc

# showValuesFromParameters
{
  :local showValue do={
    :local logLine "value='$value'"
    :put $logLine
  }

  ## fails each line that ends after \$" with a `syntax error (line 12 column 4)` (the line numbers vary)

  :put "-----------------------------start"
  $showValue value="^scripts.Function..*"
  $showValue value="^scripts.Function..*\$"
  $showValue value=("^scripts.Function..*\$")
  $showValue value="\$"
  $showValue value=("\$")
  :put "-----------------------------finish"
}

showValuesFromParameters.succeeds.output.txt

-----------------------------start
value='^scripts.Function..*'
value='^scripts.Function..*$'
value='$'
-----------------------------finish

showValuesFromParameters.succeeds.rsc

# showValuesFromParameters
{
  :local showValue do={
    :local logLine "value='$value'"
    :put $logLine
  }

  :put "-----------------------------start"
  $showValue value="^scripts.Function..*"
  $showValue value=("^scripts.Function..*\$")
  $showValue value=("\$")
  :put "-----------------------------finish"
}

showValuesFromSetInitilisation.output.txt

-----------------------------start
value='^scripts.Function..*'
value='^scripts.Function..*$'
value='^scripts.Function..*$'
value='$'
value='$'
-----------------------------finish

showValuesFromSetInitilisation.rsc

{
  :local showValuesFromSetInitilisation do={
    :local value
    :local logLine

    :set $value "^scripts.Function..*"
    :set logLine "value='$value'"
    :put $logLine

    :set $value "^scripts.Function..*\$"
    :set logLine "value='$value'"
    :put $logLine

    :set $value ("^scripts.Function..*\$")
    :set logLine "value='$value'"
    :put $logLine

    :set $value "\$"
    :set logLine "value='$value'"
    :put $logLine

    :set $value ("\$")
    :set logLine "value='$value'"
    :put $logLine
  }
  :put "-----------------------------start"
  $showValuesFromSetInitilisation
  :put "-----------------------------finish"
}