diff --git a/app/api/routes-f/iqr-outlier/route.test.ts b/app/api/routes-f/iqr-outlier/route.test.ts
new file mode 100644
index 00000000..144bbb3f
--- /dev/null
+++ b/app/api/routes-f/iqr-outlier/route.test.ts
@@ -0,0 +1,124 @@
+import { POST } from "./route";
+
+describe("IQR Outlier Detection API", () => {
+  it("should return 400 for invalid JSON", async () => {
+    const req = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: "bad json",
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(400);
+  });
+
+  it("should return 400 when data is missing", async () => {
+    const req = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({}),
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(400);
+  });
+
+  it("should return 400 when data is empty", async () => {
+    const req = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({ data: [] }),
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(400);
+  });
+
+  it("should return 400 when data contains non-numbers", async () => {
+    const req = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({ data: [1, "two", 3] }),
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(400);
+  });
+
+  it("should return 400 for a negative multiplier", async () => {
+    const req = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({ data: [1, 2, 3, 4, 5], multiplier: -1 }),
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(400);
+  });
+
+  it("detects dataset with no outliers", async () => {
+    const req = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({ data: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] }),
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(200);
+    const data = await res.json();
+    expect(data.outliers).toEqual([]);
+    expect(typeof data.q1).toBe("number");
+    expect(typeof data.q3).toBe("number");
+    expect(typeof data.iqr).toBe("number");
+    expect(typeof data.lower_bound).toBe("number");
+    expect(typeof data.upper_bound).toBe("number");
+  });
+
+  it("detects obvious outliers", async () => {
+    // Dataset: 1-10 with 100 as an outlier
+    const req = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({ data: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100] }),
+    });
+    const res = await POST(req as any);
+    const data = await res.json();
+    expect(data.outliers).toContain(100);
+  });
+
+  it("uses default multiplier of 1.5", async () => {
+    const dataset = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100];
+    const req1 = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({ data: dataset }),
+    });
+    const req2 = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({ data: dataset, multiplier: 1.5 }),
+    });
+    const [res1, res2] = await Promise.all([POST(req1 as any), POST(req2 as any)]);
+    const [d1, d2] = await Promise.all([res1.json(), res2.json()]);
+    expect(d1).toEqual(d2);
+  });
+
+  it("custom multiplier changes bounds", async () => {
+    const data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15];
+    const reqDefault = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({ data, multiplier: 1.5 }),
+    });
+    const reqStrict = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({ data, multiplier: 0.5 }),
+    });
+    const [resDefault, resStrict] = await Promise.all([
+      POST(reqDefault as any),
+      POST(reqStrict as any),
+    ]);
+    const [dDefault, dStrict] = await Promise.all([resDefault.json(), resStrict.json()]);
+    // Stricter multiplier yields narrower bounds, more outliers
+    expect(dStrict.upper_bound).toBeLessThan(dDefault.upper_bound);
+  });
+
+  it("computes correct IQR values for a known dataset", async () => {
+    // sorted: [2, 4, 6, 8, 10] → Q1=4, Q3=8, IQR=4
+    const req = new Request("http://localhost/api/routes-f/iqr-outlier", {
+      method: "POST",
+      body: JSON.stringify({ data: [10, 2, 6, 8, 4] }),
+    });
+    const res = await POST(req as any);
+    const data = await res.json();
+    expect(data.q1).toBeCloseTo(4);
+    expect(data.q3).toBeCloseTo(8);
+    expect(data.iqr).toBeCloseTo(4);
+    expect(data.lower_bound).toBeCloseTo(4 - 1.5 * 4); // -2
+    expect(data.upper_bound).toBeCloseTo(8 + 1.5 * 4); // 14
+  });
+});
diff --git a/app/api/routes-f/iqr-outlier/route.ts b/app/api/routes-f/iqr-outlier/route.ts
new file mode 100644
index 00000000..22136d60
--- /dev/null
+++ b/app/api/routes-f/iqr-outlier/route.ts
@@ -0,0 +1,54 @@
+import { type NextRequest, NextResponse } from "next/server";
+
+/**
+ * Calculates the quartile value for a sorted dataset using linear interpolation.
+ * Uses the inclusive method (same as Excel's QUARTILE.INC / NumPy default).
+ */
+function quartile(sorted: number[], q: 0.25 | 0.75): number {
+  const pos = q * (sorted.length - 1);
+  const lower = Math.floor(pos);
+  const upper = Math.ceil(pos);
+  const frac = pos - lower;
+  return sorted[lower] + frac * (sorted[upper] - sorted[lower]);
+}
+
+export async function POST(req: NextRequest) {
+  let body: unknown;
+  try {
+    body = await req.json();
+  } catch {
+    return NextResponse.json({ error: "Invalid JSON body." }, { status: 400 });
+  }
+
+  if (typeof body !== "object" || body === null || Array.isArray(body)) {
+    return NextResponse.json({ error: "Request body must be an object." }, { status: 400 });
+  }
+
+  const { data, multiplier } = body as Record<string, unknown>;
+
+  if (!Array.isArray(data) || data.length === 0 || data.some((v) => typeof v !== "number")) {
+    return NextResponse.json(
+      { error: "data must be a non-empty array of numbers." },
+      { status: 400 }
+    );
+  }
+
+  const m = multiplier !== undefined ? multiplier : 1.5;
+  if (typeof m !== "number" || m < 0) {
+    return NextResponse.json(
+      { error: "multiplier must be a non-negative number." },
+      { status: 400 }
+    );
+  }
+
+  const sorted = [...(data as number[])].sort((a, b) => a - b);
+
+  const q1 = quartile(sorted, 0.25);
+  const q3 = quartile(sorted, 0.75);
+  const iqr = q3 - q1;
+  const lower_bound = q1 - m * iqr;
+  const upper_bound = q3 + m * iqr;
+  const outliers = sorted.filter((v) => v < lower_bound || v > upper_bound);
+
+  return NextResponse.json({ q1, q3, iqr, lower_bound, upper_bound, outliers });
+}
diff --git a/app/api/routes-f/polynomial-eval/route.test.ts b/app/api/routes-f/polynomial-eval/route.test.ts
new file mode 100644
index 00000000..be33cb4c
--- /dev/null
+++ b/app/api/routes-f/polynomial-eval/route.test.ts
@@ -0,0 +1,112 @@
+import { POST } from "./route";
+
+describe("Polynomial Evaluator API", () => {
+  it("should return 400 for invalid JSON", async () => {
+    const req = new Request("http://localhost/api/routes-f/polynomial-eval", {
+      method: "POST",
+      body: "not-json",
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(400);
+    const data = await res.json();
+    expect(data.error).toBeDefined();
+  });
+
+  it("should return 400 when coefficients is missing", async () => {
+    const req = new Request("http://localhost/api/routes-f/polynomial-eval", {
+      method: "POST",
+      body: JSON.stringify({ x: 2 }),
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(400);
+  });
+
+  it("should return 400 when coefficients is empty", async () => {
+    const req = new Request("http://localhost/api/routes-f/polynomial-eval", {
+      method: "POST",
+      body: JSON.stringify({ coefficients: [], x: 2 }),
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(400);
+  });
+
+  it("should return 400 when x is not a number or array", async () => {
+    const req = new Request("http://localhost/api/routes-f/polynomial-eval", {
+      method: "POST",
+      body: JSON.stringify({ coefficients: [1, 2, 3], x: "hello" }),
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(400);
+  });
+
+  it("evaluates a constant polynomial f(x) = 5", async () => {
+    const req = new Request("http://localhost/api/routes-f/polynomial-eval", {
+      method: "POST",
+      body: JSON.stringify({ coefficients: [5], x: 10 }),
+    });
+    const res = await POST(req as any);
+    expect(res.status).toBe(200);
+    const data = await res.json();
+    expect(data.results).toEqual([5]);
+  });
+
+  it("evaluates f(x) = 2x + 1 at x=3 via Horner's method", async () => {
+    // Horner: coefficients = [2, 1], x=3 → 2*3+1 = 7
+    const req = new Request("http://localhost/api/routes-f/polynomial-eval", {
+      method: "POST",
+      body: JSON.stringify({ coefficients: [2, 1], x: 3 }),
+    });
+    const res = await POST(req as any);
+    const data = await res.json();
+    expect(data.results).toEqual([7]);
+  });
+
+  it("evaluates f(x) = 3x² + 2x + 1 at x=2 via Horner (matches expanded form)", async () => {
+    // Expanded: 3*4 + 2*2 + 1 = 17. Horner: [3,2,1], x=2 → ((3*2)+2)*2+1=17
+    const req = new Request("http://localhost/api/routes-f/polynomial-eval", {
+      method: "POST",
+      body: JSON.stringify({ coefficients: [3, 2, 1], x: 2 }),
+    });
+    const res = await POST(req as any);
+    const data = await res.json();
+    expect(data.results).toEqual([17]);
+  });
+
+  it("evaluates a polynomial at multiple x values", async () => {
+    // f(x) = x^2 = [1, 0, 0], x=[0,2,3] → [0,4,9]
+    const req = new Request("http://localhost/api/routes-f/polynomial-eval", {
+      method: "POST",
+      body: JSON.stringify({ coefficients: [1, 0, 0], x: [0, 2, 3] }),
+    });
+    const res = await POST(req as any);
+    const data = await res.json();
+    expect(data.results).toEqual([0, 4, 9]);
+  });
+
+  it("Horner result matches expanded form for degree-3 polynomial", async () => {
+    // f(x) = 2x^3 - 3x^2 + x - 5 at x=4
+    // Expanded: 2*64 - 3*16 + 4 - 5 = 128 - 48 + 4 - 5 = 79
+    const x = 4;
+    const coefficients = [2, -3, 1, -5];
+    const expanded = 2 * x ** 3 - 3 * x ** 2 + 1 * x - 5;
+
+    const req = new Request("http://localhost/api/routes-f/polynomial-eval", {
+      method: "POST",
+      body: JSON.stringify({ coefficients, x }),
+    });
+    const res = await POST(req as any);
+    const data = await res.json();
+    expect(data.results[0]).toBeCloseTo(expanded);
+  });
+
+  it("handles x=0", async () => {
+    // f(0) = constant term (last coef)
+    const req = new Request("http://localhost/api/routes-f/polynomial-eval", {
+      method: "POST",
+      body: JSON.stringify({ coefficients: [5, 3, 7], x: 0 }),
+    });
+    const res = await POST(req as any);
+    const data = await res.json();
+    expect(data.results).toEqual([7]);
+  });
+});
diff --git a/app/api/routes-f/polynomial-eval/route.ts b/app/api/routes-f/polynomial-eval/route.ts
new file mode 100644
index 00000000..6a06e226
--- /dev/null
+++ b/app/api/routes-f/polynomial-eval/route.ts
@@ -0,0 +1,50 @@
+import { type NextRequest, NextResponse } from "next/server";
+
+/**
+ * Evaluates a polynomial at a given x value using Horner's method.
+ * Coefficients are ordered highest-degree first.
+ * e.g. [3, 2, 1] represents 3x² + 2x + 1
+ */
+function horner(coefficients: number[], x: number): number {
+  return coefficients.reduce((acc, coef) => acc * x + coef, 0);
+}
+
+export async function POST(req: NextRequest) {
+  let body: unknown;
+  try {
+    body = await req.json();
+  } catch {
+    return NextResponse.json({ error: "Invalid JSON body." }, { status: 400 });
+  }
+
+  if (typeof body !== "object" || body === null || Array.isArray(body)) {
+    return NextResponse.json({ error: "Request body must be an object." }, { status: 400 });
+  }
+
+  const { coefficients, x } = body as Record<string, unknown>;
+
+  if (
+    !Array.isArray(coefficients) ||
+    coefficients.length === 0 ||
+    coefficients.some((c) => typeof c !== "number")
+  ) {
+    return NextResponse.json(
+      { error: "coefficients must be a non-empty array of numbers." },
+      { status: 400 }
+    );
+  }
+
+  const isArrayOfX = Array.isArray(x);
+  const xValues: unknown[] = isArrayOfX ? x : [x];
+
+  if (xValues.some((v) => typeof v !== "number")) {
+    return NextResponse.json(
+      { error: "x must be a number or an array of numbers." },
+      { status: 400 }
+    );
+  }
+
+  const results = (xValues as number[]).map((xVal) => horner(coefficients as number[], xVal));
+
+  return NextResponse.json({ results });
+}
diff --git a/app/api/routesF/reverse-word-order/route.test.ts b/app/api/routesF/reverse-word-order/route.test.ts
new file mode 100644
index 00000000..945ca9cb
--- /dev/null
+++ b/app/api/routesF/reverse-word-order/route.test.ts
@@ -0,0 +1,110 @@
+import { POST } from "./route";
+
+describe("Reverse Word Order API", () => {
+  it("should return 400 for invalid JSON", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: "not-json",
+    });
+    const res = await POST(req);
+    expect(res.status).toBe(400);
+  });
+
+  it("should return 400 when text is missing", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: JSON.stringify({}),
+    });
+    const res = await POST(req);
+    expect(res.status).toBe(400);
+  });
+
+  it("should return 400 when text is not a string", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: JSON.stringify({ text: 42 }),
+    });
+    const res = await POST(req);
+    expect(res.status).toBe(400);
+  });
+
+  it("reverses words in a simple sentence", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: JSON.stringify({ text: "hello world" }),
+    });
+    const res = await POST(req);
+    const data = await res.json();
+    expect(data.result).toBe("world hello");
+  });
+
+  it("collapses multiple internal spaces to a single space", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: JSON.stringify({ text: "hello   world   foo" }),
+    });
+    const res = await POST(req);
+    const data = await res.json();
+    expect(data.result).toBe("foo world hello");
+  });
+
+  it("trims leading and trailing whitespace", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: JSON.stringify({ text: "  hello world  " }),
+    });
+    const res = await POST(req);
+    const data = await res.json();
+    expect(data.result).toBe("world hello");
+  });
+
+  it("handles a single word", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: JSON.stringify({ text: "hello" }),
+    });
+    const res = await POST(req);
+    const data = await res.json();
+    expect(data.result).toBe("hello");
+  });
+
+  it("handles an empty string", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: JSON.stringify({ text: "" }),
+    });
+    const res = await POST(req);
+    const data = await res.json();
+    expect(data.result).toBe("");
+  });
+
+  it("handles a string with only whitespace", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: JSON.stringify({ text: "   " }),
+    });
+    const res = await POST(req);
+    const data = await res.json();
+    expect(data.result).toBe("");
+  });
+
+  it("handles mixed tabs and spaces", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: JSON.stringify({ text: "foo\t\tbar  baz" }),
+    });
+    const res = await POST(req);
+    const data = await res.json();
+    expect(data.result).toBe("baz bar foo");
+  });
+
+  it("reverses a multi-word sentence correctly", async () => {
+    const req = new Request("http://localhost/api/routesF/reverse-word-order", {
+      method: "POST",
+      body: JSON.stringify({ text: "the quick brown fox" }),
+    });
+    const res = await POST(req);
+    const data = await res.json();
+    expect(data.result).toBe("fox brown quick the");
+  });
+});
diff --git a/app/api/routesF/reverse-word-order/route.ts b/app/api/routesF/reverse-word-order/route.ts
new file mode 100644
index 00000000..e851a847
--- /dev/null
+++ b/app/api/routesF/reverse-word-order/route.ts
@@ -0,0 +1,36 @@
+import { NextResponse } from "next/server";
+
+/**
+ * Reverses the order of words in the given text.
+ * Collapses internal whitespace to single spaces and trims leading/trailing whitespace.
+ */
+function reverseWordOrder(text: string): string {
+  return text
+    .trim()
+    .split(/\s+/)
+    .reverse()
+    .join(" ");
+}
+
+export async function POST(request: Request) {
+  let body: unknown;
+  try {
+    body = await request.json();
+  } catch {
+    return NextResponse.json({ error: "Invalid JSON body." }, { status: 400 });
+  }
+
+  if (typeof body !== "object" || body === null || Array.isArray(body)) {
+    return NextResponse.json({ error: "Request body must be an object." }, { status: 400 });
+  }
+
+  const { text } = body as Record<string, unknown>;
+
+  if (typeof text !== "string") {
+    return NextResponse.json({ error: "text must be a string." }, { status: 400 });
+  }
+
+  const result = reverseWordOrder(text);
+
+  return NextResponse.json({ result });
+}