diff --git a/.github/workflows/test-integration.yml b/.github/workflows/test-integration.yml
index 80d5c623..c3ad506f 100644
--- a/.github/workflows/test-integration.yml
+++ b/.github/workflows/test-integration.yml
@@ -54,10 +54,18 @@ jobs:
         version:
           - input: 2.x
             expected: "Task version: 2.8.1"
-          - input: 2.8.x
-            expected: "Task version: 2.8.1"
-          - input: 3.4.1
-            expected: "Task version: 3.4.1"
+          - input: 3.36.x
+            expected: "Task version: v3.36.0 (h1:XVJ5hQ5hdzTAulHpAGzbUMUuYr9MUOEQFOFazI3hUsY=)"
+          - input: 3.37.2
+            expected: "Task version: v3.37.2 (h1:Jwgvo+2vX79Fu+44xPxVKC5DIkUE89QeDjN2tmYaQzA=)"
+
+        exclude:
+          # The macos-latest runner is an Apple Silicon machine, but Task 2.x is only available for x86 on macOS, which
+          # would cause a spurious test failure: "Unexpected HTTP response: 404"
+          - runs-on: macos-latest
+            version:
+              input: 2.x
+              expected: "Task version: 2.8.1"
 
     steps:
       - name: Checkout repository
diff --git a/__tests__/main.test.ts b/__tests__/main.test.ts
index 267533e2..094a4538 100644
--- a/__tests__/main.test.ts
+++ b/__tests__/main.test.ts
@@ -43,8 +43,8 @@ describe("installer tests", () => {
   });
 
   it("Downloads version of Task if no matching version is installed", async () => {
-    await installer.getTask("2.6.0", "");
-    const taskDir = path.join(toolDir, "task", "2.6.0", os.arch());
+    await installer.getTask("3.37.1", "");
+    const taskDir = path.join(toolDir, "task", "3.37.1", os.arch());
 
     expect(fs.existsSync(`${taskDir}.complete`)).toBe(true);
 
@@ -67,9 +67,9 @@ describe("installer tests", () => {
       nock.enableNetConnect();
     });
 
-    it("Gets the latest version of Task 2.5 using 2.5 and no matching version is installed", async () => {
-      await installer.getTask("2.5", "");
-      const taskDir = path.join(toolDir, "task", "2.5.2", os.arch());
+    it("Gets the latest version of Task 3.36 using 3.36 and no matching version is installed", async () => {
+      await installer.getTask("3.36", "");
+      const taskDir = path.join(toolDir, "task", "3.36.0", os.arch());
 
       expect(fs.existsSync(`${taskDir}.complete`)).toBe(true);
       if (IS_WINDOWS) {
@@ -79,21 +79,9 @@ describe("installer tests", () => {
       }
     });
 
-    it("Gets latest version of Task using 2.x and no matching version is installed", async () => {
-      await installer.getTask("2.x", "");
-      const taskdir = path.join(toolDir, "task", "2.6.0", os.arch());
-
-      expect(fs.existsSync(`${taskdir}.complete`)).toBe(true);
-      if (IS_WINDOWS) {
-        expect(fs.existsSync(path.join(taskdir, "bin", "task.exe"))).toBe(true);
-      } else {
-        expect(fs.existsSync(path.join(taskdir, "bin", "task"))).toBe(true);
-      }
-    });
-
-    it("Gets preview version of Task using 3.x and no matching version is installed", async () => {
+    it("Gets latest version of Task using 3.x and no matching version is installed", async () => {
       await installer.getTask("3.x", "");
-      const taskdir = path.join(toolDir, "task", "3.0.0-preview1", os.arch());
+      const taskdir = path.join(toolDir, "task", "3.37.2", os.arch());
 
       expect(fs.existsSync(`${taskdir}.complete`)).toBe(true);
       if (IS_WINDOWS) {
@@ -104,8 +92,8 @@ describe("installer tests", () => {
     });
 
     it("Skips version computing when a valid semver is provided", async () => {
-      await installer.getTask("3.0.0", "");
-      const taskdir = path.join(toolDir, "task", "3.0.0", os.arch());
+      await installer.getTask("3.37.0", "");
+      const taskdir = path.join(toolDir, "task", "3.37.0", os.arch());
 
       expect(fs.existsSync(`${taskdir}.complete`)).toBe(true);
       if (IS_WINDOWS) {
diff --git a/__tests__/testdata/tags.json b/__tests__/testdata/tags.json
index dc128c07..fbd1a376 100644
--- a/__tests__/testdata/tags.json
+++ b/__tests__/testdata/tags.json
@@ -248,5 +248,35 @@
       "type": "tag",
       "url": "https://api.github.com/repos/go-task/task/git/tags/b637b3f832f28ce254377e507170c62cce3c20da"
     }
+  },
+  {
+    "ref": "refs/tags/v3.36.0",
+    "node_id": "MDM6UmVmODMyNTI5ODM6cmVmcy90YWdzL3YzLjM2LjA=",
+    "url": "https://api.github.com/repos/go-task/task/git/refs/tags/v3.36.0",
+    "object": {
+      "sha": "cc6d0979c6584edc68623aa67ffe29742baeaefe",
+      "type": "tag",
+      "url": "https://api.github.com/repos/go-task/task/git/tags/cc6d0979c6584edc68623aa67ffe29742baeaefe"
+    }
+  },
+  {
+    "ref": "refs/tags/v3.37.1",
+    "node_id": "MDM6UmVmODMyNTI5ODM6cmVmcy90YWdzL3YzLjM3LjE=",
+    "url": "https://api.github.com/repos/go-task/task/git/refs/tags/v3.37.1",
+    "object": {
+      "sha": "e48824e99dbccf39dc7d376c2684560945123b30",
+      "type": "tag",
+      "url": "https://api.github.com/repos/go-task/task/git/tags/e48824e99dbccf39dc7d376c2684560945123b30"
+    }
+  },
+  {
+    "ref": "refs/tags/v3.37.2",
+    "node_id": "MDM6UmVmODMyNTI5ODM6cmVmcy90YWdzL3YzLjM3LjI=",
+    "url": "https://api.github.com/repos/go-task/task/git/refs/tags/v3.37.2",
+    "object": {
+      "sha": "7aa90b1511c05da43f415d3e6b27aa9866cb40cb",
+      "type": "tag",
+      "url": "https://api.github.com/repos/go-task/task/git/tags/7aa90b1511c05da43f415d3e6b27aa9866cb40cb"
+    }
   }
 ]