GNU sed, 65 59 57 bytes

Edit: 2 bytes shorter thanks to Toby Speight's comments

s/[+-]/1&/g
s/*/2&/g
s:/:d0>@2&:g
s/.*/dc -e"0[1-]s@&p"/e

###Run:

sed -f simple_calculator.sed <<< "*///*-*+-+"

###Output: -1

The sed script prepares the input for the dc shell call at the end, the latter accepting the input in Reverse Polish notation. On division, if the number is negative (d0>), the [1-] decrement command stored in register @ is called. Conversion example: + - * / --> 1+ 1- 2* d0>@2/.

GNU sed, 65 59 57 bytes

Edit: 2 bytes shorter thanks to Toby Speight's comments

s/[+-]/1&/g
s/*/2&/g
s:/:d0>@2&:g
s/.*/dc -e"0[1-]s@&p"/e

Run:

sed -f simple_calculator.sed <<< "*///*-*+-+"

Output:

-1

The sed script prepares the input for the dc shell call at the end, the latter accepting the input in Reverse Polish notation. On division, if the number is negative (d0>), the [1-] decrement command stored in register @ is called. Conversion example: + - * / --> 1+ 1- 2* d0>@2/.

GNU sed, 65 59 57 bytes

Edit: 2 bytes shorter thanks to Toby Speight's comments

s/[+-]/1&/g
s/*/2&/g
s:/:d0>@2&:g
s/.*/dc -e"0[1-]s@&p"/e

###Run:

sed -f simple_calculator.sed <<< "\*///\*-\*+-+"

###Output: -1

The sed script prepares the input for the dc shell call at the end, the latter accepting the input in Reverse Polish notation. On division, if the number is negative (d0>), the [1-] decrement command stored in register @ is called. Conversion example: + - * / --> 1+ 1- 2* d0>@2/.

GNU sed, 65 59 57 bytes

Edit: 2 bytes shorter thanks to Toby Speight's comments

s/[+-]/1&/g
s/*/2&/g
s:/:d0>@2&:g
s/.*/dc -e"0[1-]s@&p"/e

###Run:

sed -f simple_calculator.sed <<< "*///*-*+-+"

###Output: -1

The sed script prepares the input for the dc shell call at the end, the latter accepting the input in Reverse Polish notation. On division, if the number is negative (d0>), the [1-] decrement command stored in register @ is called. Conversion example: + - * / --> 1+ 1- 2* d0>@2/.

GNU sed, 65 59 57 bytes

Edit: 2 bytes shorter thanks to Toby Speight's comments

s/[+-]/1&/g
s/*/2&/g
s:/:d0>@2&:g
s/.*/dc -e"0[1-]s@&p"/e

Run: sed -f simple_calculator.sed <<< "*///*-*+-+"

Output:
-1

The sed script prepares the input for the dc shell call at the end, the latter accepting the input in Reverse Polish notation. On division, if the number is negative (d0>), the [1-] decrement command stored in registry @ is called. Conversion example: + - * / --> 1+ 1- 2* d0>@2/.

GNU sed, 65 59 57 bytes

Edit: 2 bytes shorter thanks to Toby Speight's comments

s/[+-]/1&/g
s/*/2&/g
s:/:d0>@2&:g
s/.*/dc -e"0[1-]s@&p"/e

###Run:

sed -f simple_calculator.sed <<< "\*///\*-\*+-+"

###Output: -1

The sed script prepares the input for the dc shell call at the end, the latter accepting the input in Reverse Polish notation. On division, if the number is negative (d0>), the [1-] decrement command stored in register @ is called. Conversion example: + - * / --> 1+ 1- 2* d0>@2/.