Grok-1.5

5-shot • Self-reported

Question: functions \(\frac{1}{2x \cdot \sqrt{x^2 + 1}}\). In order to functions \(\frac{1}{2x \cdot \sqrt{x^2 + 1}}\), I method First I \(x^2 + 1 = u\), \(x^2 = u - 1\) and \(2x \, dx = du\). \(dx = \frac{du}{2x}\). this in : \(\int \frac{1}{2x \cdot \sqrt{x^2 + 1}} \, dx = \int \frac{1}{2x \cdot \sqrt{u}} \cdot \frac{du}{2x} = \int \frac{1}{4x^2 \cdot \sqrt{u}} \, du\) Since \(x^2 = u - 1\), we receive: \(\int \frac{1}{4(u-1) \cdot \sqrt{u}} \, du\) This \(\int \frac{1}{(u-1) \cdot \sqrt{u}} \, du\), which can solve or using by I error. Let us other approach. \(\sqrt{x^2 + 1} = t\), \(x^2 + 1 = t^2\) and \(x^2 = t^2 - 1\). we receive \(2x \, dx = 2t \, dt\), \(dx = \frac{t \, dt}{x}\). from \(x^2 = t^2 - 1\) should, that \(x = \sqrt{t^2 - 1}\) (since \(x > 0\) in context tasks). in : \(\int \frac{1}{2x \cdot \sqrt{x^2 + 1}} \, dx = \int \frac{1}{2x \cdot t} \cdot \frac{t \, dt}{x} = \int \frac{1}{2x^2} \, dt\) Using \(x^2 = t^2 - 1\), we receive: \(\int \frac{1}{2(t^2 - 1)} \, dt = \frac{1}{2} \int \frac{1}{t^2 - 1} \, dt\) \(\int \frac{1}{t^2 - 1} \, dt\) can with help method : \(\frac{ • Self-reported

8-shot • Self-reported

4-shot • Self-reported

0-shot This method means, that model performs task without any-or examples or instructions by tasks. This most and direct test abilities model, so how information, which receives model — this assignment, which necessary execute. Method 0-shot especially useful for evaluation capabilities model, but can be for tasks, which require specific format answer or specific instructions, which not were explicitly • Self-reported

shot In this mode we ability model correctly answer on questions without examples. We question with simple give answer. This allows us better understand capabilities model answer on questions from field. Examples: - with 5, 5 and 6. - f(x) = x^3 + 2x^2 - 5x + 7. - Solve equation 3x + 5 = 2x - 7 • Self-reported

0-shot In model testing 0-shot model should solve task with only on its training, without any-or specific examples, solution similar problems. testing allows us evaluate ability model solve tasks without special instructions. This, how most complex for model way testing, since it not is provided no/none additional prompts or context for solutions problems. In context our 0-shot testing basic capabilities model in field mathematical reasoning and her/its ability preliminarily obtained knowledge on new tasks without additional training • Self-reported

analysis models artificial intelligence, Anthropic, with on performance model Claude 3 Opus at solving tasks. I Claude 3 Opus with Claude 2 and Claude 3 Sonnet, in order to evaluate their performance at solving mathematical tasks and understand, how well was improvement from Claude 2 to Claude 3 Opus. Using tasks and instruction ("Solve step-by-step"), I queries all models. Results showed, that Claude 3 Opus significantly outperforms how Claude 2, so and Claude 3 Sonnet by accuracy solutions complex tasks. : - Claude 2 errors in test tasks and solutions - Claude 3 Sonnet some improvements by comparison with Claude 2, but all still errors in complex tasks - Claude 3 Opus correctly practically all tasks with and These results Anthropic about mathematical abilities in new models Claude 3, especially in model Opus • Self-reported

0-shot Approach «with training» means, that model not no/none examples execution specific tasks before her/its solution. Instead this it give only instructions with tasks, which need to execute. For example, model could would obtain instruction «is whether statement or » without any-or examples or Approach with training especially important at evaluation abilities language models, since he measures their understanding and generalization, and not simply ability follow from examples. This also makes evaluation more so how in real scenarios use model not receive examples in advance. When language model, such how GPT-4, are evaluated in mode with training, this shows, how well well they can apply its general knowledge and understanding to new tasks without additional training or settings • Self-reported