curl --request POST \
  --url http://{host}:{port}/{contextPath}/execution/{id}/localVariables \
  --header 'Authorization: Basic <encoded-value>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "modifications": {
    "aVariable": {
      "value": "aValue",
      "type": "String"
    },
    "anotherVariable": {
      "value": 42,
      "type": "Integer"
    }
  },
  "deletions": [
    "aThirdVariable",
    "FourthVariable"
  ]
}
'

import requests

url = "http://{host}:{port}/{contextPath}/execution/{id}/localVariables"

payload = {
    "modifications": {
        "aVariable": {
            "value": "aValue",
            "type": "String"
        },
        "anotherVariable": {
            "value": 42,
            "type": "Integer"
        }
    },
    "deletions": ["aThirdVariable", "FourthVariable"]
}
headers = {
    "Authorization": "Basic <encoded-value>",
    "Content-Type": "application/json"
}

response = requests.post(url, json=payload, headers=headers)

print(response.text)

const options = {
  method: 'POST',
  headers: {Authorization: 'Basic <encoded-value>', 'Content-Type': 'application/json'},
  body: JSON.stringify({
    modifications: {
      aVariable: {value: 'aValue', type: 'String'},
      anotherVariable: {value: 42, type: 'Integer'}
    },
    deletions: ['aThirdVariable', 'FourthVariable']
  })
};

fetch('http://{host}:{port}/{contextPath}/execution/{id}/localVariables', options)
  .then(res => res.json())
  .then(res => console.log(res))
  .catch(err => console.error(err));

<?php

$curl = curl_init();

curl_setopt_array($curl, [
  CURLOPT_PORT => "62437",
  CURLOPT_URL => "http://{host}:{port}/{contextPath}/execution/{id}/localVariables",
  CURLOPT_RETURNTRANSFER => true,
  CURLOPT_ENCODING => "",
  CURLOPT_MAXREDIRS => 10,
  CURLOPT_TIMEOUT => 30,
  CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
  CURLOPT_CUSTOMREQUEST => "POST",
  CURLOPT_POSTFIELDS => json_encode([
    'modifications' => [
        'aVariable' => [
                'value' => 'aValue',
                'type' => 'String'
        ],
        'anotherVariable' => [
                'value' => 42,
                'type' => 'Integer'
        ]
    ],
    'deletions' => [
        'aThirdVariable',
        'FourthVariable'
    ]
  ]),
  CURLOPT_HTTPHEADER => [
    "Authorization: Basic <encoded-value>",
    "Content-Type: application/json"
  ],
]);

$response = curl_exec($curl);
$err = curl_error($curl);

curl_close($curl);

if ($err) {
  echo "cURL Error #:" . $err;
} else {
  echo $response;
}

package main

import (
	"fmt"
	"strings"
	"net/http"
	"io"
)

func main() {

	url := "http://{host}:{port}/{contextPath}/execution/{id}/localVariables"

	payload := strings.NewReader("{\n  \"modifications\": {\n    \"aVariable\": {\n      \"value\": \"aValue\",\n      \"type\": \"String\"\n    },\n    \"anotherVariable\": {\n      \"value\": 42,\n      \"type\": \"Integer\"\n    }\n  },\n  \"deletions\": [\n    \"aThirdVariable\",\n    \"FourthVariable\"\n  ]\n}")

	req, _ := http.NewRequest("POST", url, payload)

	req.Header.Add("Authorization", "Basic <encoded-value>")
	req.Header.Add("Content-Type", "application/json")

	res, _ := http.DefaultClient.Do(req)

	defer res.Body.Close()
	body, _ := io.ReadAll(res.Body)

	fmt.Println(string(body))

}

HttpResponse<String> response = Unirest.post("http://{host}:{port}/{contextPath}/execution/{id}/localVariables")
  .header("Authorization", "Basic <encoded-value>")
  .header("Content-Type", "application/json")
  .body("{\n  \"modifications\": {\n    \"aVariable\": {\n      \"value\": \"aValue\",\n      \"type\": \"String\"\n    },\n    \"anotherVariable\": {\n      \"value\": 42,\n      \"type\": \"Integer\"\n    }\n  },\n  \"deletions\": [\n    \"aThirdVariable\",\n    \"FourthVariable\"\n  ]\n}")
  .asString();

require 'uri'
require 'net/http'

url = URI("http://{host}:{port}/{contextPath}/execution/{id}/localVariables")

http = Net::HTTP.new(url.host, url.port)

request = Net::HTTP::Post.new(url)
request["Authorization"] = 'Basic <encoded-value>'
request["Content-Type"] = 'application/json'
request.body = "{\n  \"modifications\": {\n    \"aVariable\": {\n      \"value\": \"aValue\",\n      \"type\": \"String\"\n    },\n    \"anotherVariable\": {\n      \"value\": 42,\n      \"type\": \"Integer\"\n    }\n  },\n  \"deletions\": [\n    \"aThirdVariable\",\n    \"FourthVariable\"\n  ]\n}"

response = http.request(request)
puts response.read_body

{
  "type": "<string>",
  "message": "<string>",
  "code": 123
}

{
  "type": "<string>",
  "message": "<string>",
  "code": 123
}